Solve for u -1/5u+2-u=1/2u+3+4/5u

$- \frac{1}{5} u + 2 - u = \frac{1}{2} u + 3 + \frac{4}{5} u$

Simplify $- \frac{1}{5} u + 2 - u$ .

Combine $u$ and $\frac{1}{5}$ .

$- \frac{u}{5} + 2 - u = \frac{1}{2} u + 3 + \frac{4}{5} u$

To write $- u$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{u}{5} - u \cdot \frac{5}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Simplify terms.

Combine $- u$ and $\frac{5}{5}$ .

$- \frac{u}{5} + \frac{- u \cdot 5}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Combine the numerators over the common denominator.

$\frac{- u - u \cdot 5}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Simplify each term.

Simplify the numerator.

Factor $u$ out of $- u - u \cdot 5$ .

Factor $u$ out of $- u$ .

$\frac{u \cdot - 1 - u \cdot 5}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Factor $u$ out of $- u \cdot 5$ .

$\frac{u \cdot - 1 + u (- 1 \cdot 5)}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Factor $u$ out of $u \cdot - 1 + u (- 1 \cdot 5)$ .

$\frac{u (- 1 - 1 \cdot 5)}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Multiply $- 1$ by $5$ .

$\frac{u (- 1 - 5)}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Subtract $5$ from $- 1$ .

$\frac{u \cdot - 6}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Move $- 6$ to the left of $u$ .

$\frac{- 6 \cdot u}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Move the negative in front of the fraction.

$- \frac{6 u}{5} + 2 = \frac{1}{2} u + 3 + \frac{4}{5} u$

Simplify $\frac{1}{2} u + 3 + \frac{4}{5} u$ .

Simplify each term.

Combine $\frac{1}{2}$ and $u$ .

$- \frac{6 u}{5} + 2 = \frac{u}{2} + 3 + \frac{4}{5} u$

Combine $\frac{4}{5}$ and $u$ .

$- \frac{6 u}{5} + 2 = \frac{u}{2} + 3 + \frac{4 u}{5}$

To write $\frac{u}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{6 u}{5} + 2 = \frac{u}{2} \cdot \frac{5}{5} + \frac{4 u}{5} + 3$

To write $\frac{4 u}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{6 u}{5} + 2 = \frac{u}{2} \cdot \frac{5}{5} + \frac{4 u}{5} \cdot \frac{2}{2} + 3$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{u}{2}$ by $\frac{5}{5}$ .

$- \frac{6 u}{5} + 2 = \frac{u \cdot 5}{2 \cdot 5} + \frac{4 u}{5} \cdot \frac{2}{2} + 3$

Multiply $2$ by $5$ .

$- \frac{6 u}{5} + 2 = \frac{u \cdot 5}{10} + \frac{4 u}{5} \cdot \frac{2}{2} + 3$

Multiply $\frac{4 u}{5}$ by $\frac{2}{2}$ .

$- \frac{6 u}{5} + 2 = \frac{u \cdot 5}{10} + \frac{4 u \cdot 2}{5 \cdot 2} + 3$

Multiply $5$ by $2$ .

$- \frac{6 u}{5} + 2 = \frac{u \cdot 5}{10} + \frac{4 u \cdot 2}{10} + 3$

Combine the numerators over the common denominator.

$- \frac{6 u}{5} + 2 = \frac{u \cdot 5 + 4 u \cdot 2}{10} + 3$

Simplify each term.

Simplify the numerator.

Factor $u$ out of $u \cdot 5 + 4 u \cdot 2$ .

Factor $u$ out of $u \cdot 5$ .

$- \frac{6 u}{5} + 2 = \frac{u (5) + 4 u \cdot 2}{10} + 3$

Factor $u$ out of $4 u \cdot 2$ .

$- \frac{6 u}{5} + 2 = \frac{u (5) + u (4 \cdot 2)}{10} + 3$

Factor $u$ out of $u (5) + u (4 \cdot 2)$ .

$- \frac{6 u}{5} + 2 = \frac{u (5 + 4 \cdot 2)}{10} + 3$

Multiply $4$ by $2$ .

$- \frac{6 u}{5} + 2 = \frac{u (5 + 8)}{10} + 3$

Add $5$ and $8$ .

$- \frac{6 u}{5} + 2 = \frac{u \cdot 13}{10} + 3$

Move $13$ to the left of $u$ .

$- \frac{6 u}{5} + 2 = \frac{13 u}{10} + 3$

Move all terms containing $u$ to the left side of the equation.

Subtract $\frac{13 u}{10}$ from both sides of the equation.

$- \frac{6 u}{5} + 2 - \frac{13 u}{10} = 3$

To write $- \frac{6 u}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{6 u}{5} \cdot \frac{2}{2} - \frac{13 u}{10} + 2 = 3$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{6 u}{5}$ by $\frac{2}{2}$ .

$- \frac{6 u \cdot 2}{5 \cdot 2} - \frac{13 u}{10} + 2 = 3$

Multiply $5$ by $2$ .

$- \frac{6 u \cdot 2}{10} - \frac{13 u}{10} + 2 = 3$

Combine the numerators over the common denominator.

$\frac{- 6 u \cdot 2 - 13 u}{10} + 2 = 3$

Simplify each term.

Simplify the numerator.

Factor $u$ out of $- 6 u \cdot 2 - 13 u$ .

Factor $u$ out of $- 6 u \cdot 2$ .

$\frac{u (- 6 \cdot 2) - 13 u}{10} + 2 = 3$

Factor $u$ out of $- 13 u$ .

$\frac{u (- 6 \cdot 2) + u \cdot - 13}{10} + 2 = 3$

Factor $u$ out of $u (- 6 \cdot 2) + u \cdot - 13$ .

$\frac{u (- 6 \cdot 2 - 13)}{10} + 2 = 3$

Multiply $- 6$ by $2$ .

$\frac{u (- 12 - 13)}{10} + 2 = 3$

Subtract $13$ from $- 12$ .

$\frac{u \cdot - 25}{10} + 2 = 3$

Cancel the common factor of $- 25$ and $10$ .

Factor $5$ out of $u \cdot - 25$ .

$\frac{5 (u \cdot - 5)}{10} + 2 = 3$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (u \cdot - 5)}{5 (2)} + 2 = 3$

Cancel the common factor.

$\frac{5 (u \cdot - 5)}{5 \cdot 2} + 2 = 3$

Rewrite the expression.

$\frac{u \cdot - 5}{2} + 2 = 3$

Move $- 5$ to the left of $u$ .

$\frac{- 5 \cdot u}{2} + 2 = 3$

Move the negative in front of the fraction.

$- \frac{5 u}{2} + 2 = 3$

Move all terms not containing $u$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$- \frac{5 u}{2} = 3 - 2$

Subtract $2$ from $3$ .

$- \frac{5 u}{2} = 1$

Multiply both sides of the equation by $- \frac{2}{5}$ .

$- \frac{2}{5} (- \frac{5 u}{2}) = - \frac{2}{5} \cdot 1$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{5} (- \frac{5 u}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{- 2}{5} (- \frac{5 u}{2}) = - \frac{2}{5} \cdot 1$

Move the leading negative in $- \frac{5 u}{2}$ into the numerator.

$\frac{- 2}{5} \cdot \frac{- 5 u}{2} = - \frac{2}{5} \cdot 1$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{5} \cdot \frac{- 5 u}{2} = - \frac{2}{5} \cdot 1$

Cancel the common factor.

$\frac{2 \cdot - 1}{5} \cdot \frac{- 5 u}{2} = - \frac{2}{5} \cdot 1$

Rewrite the expression.

$\frac{- 1}{5} (- 5 u) = - \frac{2}{5} \cdot 1$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 u$ .

$\frac{- 1}{5} (5 (- u)) = - \frac{2}{5} \cdot 1$

Cancel the common factor.

$\frac{- 1}{5} (5 (- u)) = - \frac{2}{5} \cdot 1$

Rewrite the expression.

$- - u = - \frac{2}{5} \cdot 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 u = - \frac{2}{5} \cdot 1$

Multiply $u$ by $1$ .

$u = - \frac{2}{5} \cdot 1$

Simplify the right side.

Multiply $- 1$ by $1$ .

$u = - \frac{2}{5}$

The result can be shown in multiple forms.

Exact Form:

$u = - \frac{2}{5}$

Decimal Form:

$u = - 0.4$

Solve for u -1/5u+2-u=1/2u+3+4/5u

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