Solve for n 2/5n+3-7/10n=3/5-3n

$\frac{2}{5} n + 3 - \frac{7}{10} n = \frac{3}{5} - 3 n$

Simplify $\frac{2}{5} n + 3 - \frac{7}{10} n$ .

Simplify each term.

Combine $\frac{2}{5}$ and $n$ .

$\frac{2 n}{5} + 3 - \frac{7}{10} n = \frac{3}{5} - 3 n$

Combine $n$ and $\frac{7}{10}$ .

$\frac{2 n}{5} + 3 - \frac{n \cdot 7}{10} = \frac{3}{5} - 3 n$

Move $7$ to the left of $n$ .

$\frac{2 n}{5} + 3 - \frac{7 n}{10} = \frac{3}{5} - 3 n$

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

$\frac{2 n}{5} \cdot \frac{2}{2} - \frac{7 n}{10} + 3 = \frac{3}{5} - 3 n$

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

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

$\frac{2 n \cdot 2}{5 \cdot 2} - \frac{7 n}{10} + 3 = \frac{3}{5} - 3 n$

Multiply $5$ by $2$ .

$\frac{2 n \cdot 2}{10} - \frac{7 n}{10} + 3 = \frac{3}{5} - 3 n$

Combine the numerators over the common denominator.

$\frac{2 n \cdot 2 - 7 n}{10} + 3 = \frac{3}{5} - 3 n$

Simplify each term.

Simplify the numerator.

Factor $n$ out of $2 n \cdot 2 - 7 n$ .

Factor $n$ out of $2 n \cdot 2$ .

$\frac{n (2 \cdot 2) - 7 n}{10} + 3 = \frac{3}{5} - 3 n$

Factor $n$ out of $- 7 n$ .

$\frac{n (2 \cdot 2) + n \cdot - 7}{10} + 3 = \frac{3}{5} - 3 n$

Factor $n$ out of $n (2 \cdot 2) + n \cdot - 7$ .

$\frac{n (2 \cdot 2 - 7)}{10} + 3 = \frac{3}{5} - 3 n$

Multiply $2$ by $2$ .

$\frac{n (4 - 7)}{10} + 3 = \frac{3}{5} - 3 n$

Subtract $7$ from $4$ .

$\frac{n \cdot - 3}{10} + 3 = \frac{3}{5} - 3 n$

Move $- 3$ to the left of $n$ .

$\frac{- 3 \cdot n}{10} + 3 = \frac{3}{5} - 3 n$

Move the negative in front of the fraction.

$- \frac{3 n}{10} + 3 = \frac{3}{5} - 3 n$

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

Add $3 n$ to both sides of the equation.

$- \frac{3 n}{10} + 3 + 3 n = \frac{3}{5}$

To write $3 n$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$- \frac{3 n}{10} + 3 n \cdot \frac{10}{10} + 3 = \frac{3}{5}$

Combine $3 n$ and $\frac{10}{10}$ .

$- \frac{3 n}{10} + \frac{3 n \cdot 10}{10} + 3 = \frac{3}{5}$

Combine the numerators over the common denominator.

$\frac{- 3 n + 3 n \cdot 10}{10} + 3 = \frac{3}{5}$

Simplify the numerator.

Factor $3 n$ out of $- 3 n + 3 n \cdot 10$ .

Factor $3 n$ out of $- 3 n$ .

$\frac{3 n (- 1) + 3 n \cdot 10}{10} + 3 = \frac{3}{5}$

Factor $3 n$ out of $3 n \cdot 10$ .

$\frac{3 n (- 1) + 3 n (10)}{10} + 3 = \frac{3}{5}$

Factor $3 n$ out of $3 n (- 1) + 3 n (10)$ .

$\frac{3 n (- 1 + 10)}{10} + 3 = \frac{3}{5}$

Add $- 1$ and $10$ .

$\frac{3 n \cdot 9}{10} + 3 = \frac{3}{5}$

Multiply $9$ by $3$ .

$\frac{27 n}{10} + 3 = \frac{3}{5}$

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

Subtract $3$ from both sides of the equation.

$\frac{27 n}{10} = \frac{3}{5} - 3$

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{27 n}{10} = \frac{3}{5} - 3 \cdot \frac{5}{5}$

Combine $- 3$ and $\frac{5}{5}$ .

$\frac{27 n}{10} = \frac{3}{5} + \frac{- 3 \cdot 5}{5}$

Combine the numerators over the common denominator.

$\frac{27 n}{10} = \frac{3 - 3 \cdot 5}{5}$

Simplify the numerator.

Multiply $- 3$ by $5$ .

$\frac{27 n}{10} = \frac{3 - 15}{5}$

Subtract $15$ from $3$ .

$\frac{27 n}{10} = \frac{- 12}{5}$

Move the negative in front of the fraction.

$\frac{27 n}{10} = - \frac{12}{5}$

Multiply both sides of the equation by $\frac{10}{27}$ .

$\frac{10}{27} \cdot \frac{27 n}{10} = \frac{10}{27} (- \frac{12}{5})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{10}{27} \cdot \frac{27 n}{10}$ .

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10}{27} \cdot \frac{27 n}{10} = \frac{10}{27} (- \frac{12}{5})$

Rewrite the expression.

$\frac{1}{27} (27 n) = \frac{10}{27} (- \frac{12}{5})$

Cancel the common factor of $27$ .

Factor $27$ out of $27 n$ .

$\frac{1}{27} (27 (n)) = \frac{10}{27} (- \frac{12}{5})$

Cancel the common factor.

$\frac{1}{27} (27 n) = \frac{10}{27} (- \frac{12}{5})$

Rewrite the expression.

$n = \frac{10}{27} (- \frac{12}{5})$

Simplify the right side.

Simplify $\frac{10}{27} (- \frac{12}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{12}{5}$ into the numerator.

$n = \frac{10}{27} \cdot \frac{- 12}{5}$

Factor $5$ out of $10$ .

$n = \frac{5 (2)}{27} \cdot \frac{- 12}{5}$

Cancel the common factor.

$n = \frac{5 \cdot 2}{27} \cdot \frac{- 12}{5}$

Rewrite the expression.

$n = \frac{2}{27} \cdot - 12$

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

$n = \frac{2}{3 (9)} \cdot - 12$

Factor $3$ out of $- 12$ .

$n = \frac{2}{3 \cdot 9} \cdot (3 \cdot - 4)$

Cancel the common factor.

$n = \frac{2}{3 \cdot 9} \cdot (3 \cdot - 4)$

Rewrite the expression.

$n = \frac{2}{9} \cdot - 4$

Combine $\frac{2}{9}$ and $- 4$ .

$n = \frac{2 \cdot - 4}{9}$

Simplify the expression.

Multiply $2$ by $- 4$ .

$n = \frac{- 8}{9}$

Move the negative in front of the fraction.

$n = - \frac{8}{9}$

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{8}{9}$

Decimal Form:

$n = - 0.\overline{8}$

Solve for n 2/5n+3-7/10n=3/5-3n

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