Solve for n -1/2(5n-6)=-6(-2n-5)

$- \frac{1}{2} (5 n - 6) = - 6 (- 2 n - 5)$

Simplify $- \frac{1}{2} \cdot (5 n - 6)$ .

Start simplifying.

$0 + 0 - \frac{1}{2} \cdot (5 n - 6) = - 6 (- 2 n - 5)$

Simplify by adding zeros.

$- \frac{1}{2} \cdot (5 n - 6) = - 6 (- 2 n - 5)$

Apply the distributive property.

$- \frac{1}{2} (5 n) - \frac{1}{2} \cdot - 6 = - 6 (- 2 n - 5)$

Multiply $- \frac{1}{2} (5 n)$ .

Multiply $5$ by $- 1$ .

$- 5 (\frac{1}{2}) n - \frac{1}{2} \cdot - 6 = - 6 (- 2 n - 5)$

Combine $- 5$ and $\frac{1}{2}$ .

$\frac{- 5}{2} n - \frac{1}{2} \cdot - 6 = - 6 (- 2 n - 5)$

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

$\frac{- 5 n}{2} - \frac{1}{2} \cdot - 6 = - 6 (- 2 n - 5)$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 5 n}{2} + \frac{- 1}{2} \cdot - 6 = - 6 (- 2 n - 5)$

Factor $2$ out of $- 6$ .

$\frac{- 5 n}{2} + \frac{- 1}{2} \cdot (2 (- 3)) = - 6 (- 2 n - 5)$

Cancel the common factor.

$\frac{- 5 n}{2} + \frac{- 1}{2} \cdot (2 \cdot - 3) = - 6 (- 2 n - 5)$

Rewrite the expression.

$\frac{- 5 n}{2} - 1 \cdot - 3 = - 6 (- 2 n - 5)$

Multiply $- 1$ by $- 3$ .

$\frac{- 5 n}{2} + 3 = - 6 (- 2 n - 5)$

Move the negative in front of the fraction.

$- \frac{5 n}{2} + 3 = - 6 (- 2 n - 5)$

Simplify $- 6 (- 2 n - 5)$ .

Apply the distributive property.

$- \frac{5 n}{2} + 3 = - 6 (- 2 n) - 6 \cdot - 5$

Multiply.

Multiply $- 2$ by $- 6$ .

$- \frac{5 n}{2} + 3 = 12 n - 6 \cdot - 5$

Multiply $- 6$ by $- 5$ .

$- \frac{5 n}{2} + 3 = 12 n + 30$

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

Subtract $12 n$ from both sides of the equation.

$- \frac{5 n}{2} + 3 - 12 n = 30$

To write $- 12 n$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{5 n}{2} - 12 n \cdot \frac{2}{2} + 3 = 30$

Combine $- 12 n$ and $\frac{2}{2}$ .

$- \frac{5 n}{2} + \frac{- 12 n \cdot 2}{2} + 3 = 30$

Combine the numerators over the common denominator.

$\frac{- 5 n - 12 n \cdot 2}{2} + 3 = 30$

Simplify each term.

Simplify the numerator.

Factor $n$ out of $- 5 n - 12 n \cdot 2$ .

Factor $n$ out of $- 5 n$ .

$\frac{n \cdot - 5 - 12 n \cdot 2}{2} + 3 = 30$

Factor $n$ out of $- 12 n \cdot 2$ .

$\frac{n \cdot - 5 + n (- 12 \cdot 2)}{2} + 3 = 30$

Factor $n$ out of $n \cdot - 5 + n (- 12 \cdot 2)$ .

$\frac{n (- 5 - 12 \cdot 2)}{2} + 3 = 30$

Multiply $- 12$ by $2$ .

$\frac{n (- 5 - 24)}{2} + 3 = 30$

Subtract $24$ from $- 5$ .

$\frac{n \cdot - 29}{2} + 3 = 30$

Move $- 29$ to the left of $n$ .

$\frac{- 29 \cdot n}{2} + 3 = 30$

Move the negative in front of the fraction.

$- \frac{29 n}{2} + 3 = 30$

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

Subtract $3$ from both sides of the equation.

$- \frac{29 n}{2} = 30 - 3$

Subtract $3$ from $30$ .

$- \frac{29 n}{2} = 27$

Multiply both sides of the equation by $- \frac{2}{29}$ .

$- \frac{2}{29} (- \frac{29 n}{2}) = - \frac{2}{29} \cdot 27$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{2}{29} (- \frac{29 n}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{29}$ into the numerator.

$\frac{- 2}{29} (- \frac{29 n}{2}) = - \frac{2}{29} \cdot 27$

Move the leading negative in $- \frac{29 n}{2}$ into the numerator.

$\frac{- 2}{29} \cdot \frac{- 29 n}{2} = - \frac{2}{29} \cdot 27$

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{29} \cdot \frac{- 29 n}{2} = - \frac{2}{29} \cdot 27$

Cancel the common factor.

$\frac{2 \cdot - 1}{29} \cdot \frac{- 29 n}{2} = - \frac{2}{29} \cdot 27$

Rewrite the expression.

$\frac{- 1}{29} (- 29 n) = - \frac{2}{29} \cdot 27$

Cancel the common factor of $29$ .

Factor $29$ out of $- 29 n$ .

$\frac{- 1}{29} (29 (- n)) = - \frac{2}{29} \cdot 27$

Cancel the common factor.

$\frac{- 1}{29} (29 (- n)) = - \frac{2}{29} \cdot 27$

Rewrite the expression.

$- - n = - \frac{2}{29} \cdot 27$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 n = - \frac{2}{29} \cdot 27$

Multiply $n$ by $1$ .

$n = - \frac{2}{29} \cdot 27$

Simplify the right side.

Simplify $- \frac{2}{29} \cdot 27$ .

Multiply $- \frac{2}{29} \cdot 27$ .

Multiply $27$ by $- 1$ .

$n = - 27 (\frac{2}{29})$

Combine $- 27$ and $\frac{2}{29}$ .

$n = \frac{- 27 \cdot 2}{29}$

Multiply $- 27$ by $2$ .

$n = \frac{- 54}{29}$

Move the negative in front of the fraction.

$n = - \frac{54}{29}$

The result can be shown in multiple forms.

Exact Form:

$n = - \frac{54}{29}$

Decimal Form:

$n = - 1.86206896 \dots$

Mixed Number Form:

$n = - 1 \frac{25}{29}$

Solve for n -1/2(5n-6)=-6(-2n-5)

Related Questions

Support LCMGCF.com by disabling your adblocker.