Solve for n 2/3(n-6)=5n-43

$\frac{2}{3} (n - 6) = 5 n - 43$

Simplify $\frac{2}{3} \cdot (n - 6)$ .

Rewrite.

$0 + 0 + \frac{2}{3} \cdot (n - 6) = 5 n - 43$

Simplify by adding zeros.

$\frac{2}{3} \cdot (n - 6) = 5 n - 43$

Apply the distributive property.

$\frac{2}{3} n + \frac{2}{3} \cdot - 6 = 5 n - 43$

Combine $\frac{2}{3}$ and $n$ .

$\frac{2 n}{3} + \frac{2}{3} \cdot - 6 = 5 n - 43$

Cancel the common factor of $3$ .

Factor $3$ out of $- 6$ .

$\frac{2 n}{3} + \frac{2}{3} \cdot (3 (- 2)) = 5 n - 43$

Cancel the common factor.

$\frac{2 n}{3} + \frac{2}{3} \cdot (3 \cdot - 2) = 5 n - 43$

Rewrite the expression.

$\frac{2 n}{3} + 2 \cdot - 2 = 5 n - 43$

Multiply $2$ by $- 2$ .

$\frac{2 n}{3} - 4 = 5 n - 43$

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

Subtract $5 n$ from both sides of the equation.

$\frac{2 n}{3} - 4 - 5 n = - 43$

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

$\frac{2 n}{3} - 5 n \cdot \frac{3}{3} - 4 = - 43$

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

$\frac{2 n}{3} + \frac{- 5 n \cdot 3}{3} - 4 = - 43$

Combine the numerators over the common denominator.

$\frac{2 n - 5 n \cdot 3}{3} - 4 = - 43$

Simplify each term.

Simplify the numerator.

Factor $n$ out of $2 n - 5 n \cdot 3$ .

Factor $n$ out of $2 n$ .

$\frac{n \cdot 2 - 5 n \cdot 3}{3} - 4 = - 43$

Factor $n$ out of $- 5 n \cdot 3$ .

$\frac{n \cdot 2 + n (- 5 \cdot 3)}{3} - 4 = - 43$

Factor $n$ out of $n \cdot 2 + n (- 5 \cdot 3)$ .

$\frac{n (2 - 5 \cdot 3)}{3} - 4 = - 43$

Multiply $- 5$ by $3$ .

$\frac{n (2 - 15)}{3} - 4 = - 43$

Subtract $15$ from $2$ .

$\frac{n \cdot - 13}{3} - 4 = - 43$

Move $- 13$ to the left of $n$ .

$\frac{- 13 \cdot n}{3} - 4 = - 43$

Move the negative in front of the fraction.

$- \frac{13 n}{3} - 4 = - 43$

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

Add $4$ to both sides of the equation.

$- \frac{13 n}{3} = - 43 + 4$

Add $- 43$ and $4$ .

$- \frac{13 n}{3} = - 39$

Multiply both sides of the equation by $- \frac{3}{13}$ .

$- \frac{3}{13} (- \frac{13 n}{3}) = - \frac{3}{13} \cdot - 39$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{13} (- \frac{13 n}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{13}$ into the numerator.

$\frac{- 3}{13} (- \frac{13 n}{3}) = - \frac{3}{13} \cdot - 39$

Move the leading negative in $- \frac{13 n}{3}$ into the numerator.

$\frac{- 3}{13} \cdot \frac{- 13 n}{3} = - \frac{3}{13} \cdot - 39$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{13} \cdot \frac{- 13 n}{3} = - \frac{3}{13} \cdot - 39$

Cancel the common factor.

$\frac{3 \cdot - 1}{13} \cdot \frac{- 13 n}{3} = - \frac{3}{13} \cdot - 39$

Rewrite the expression.

$\frac{- 1}{13} (- 13 n) = - \frac{3}{13} \cdot - 39$

Cancel the common factor of $13$ .

Factor $13$ out of $- 13 n$ .

$\frac{- 1}{13} (13 (- n)) = - \frac{3}{13} \cdot - 39$

Cancel the common factor.

$\frac{- 1}{13} (13 (- n)) = - \frac{3}{13} \cdot - 39$

Rewrite the expression.

$- - n = - \frac{3}{13} \cdot - 39$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 n = - \frac{3}{13} \cdot - 39$

Multiply $n$ by $1$ .

$n = - \frac{3}{13} \cdot - 39$

Simplify the right side.

Simplify $- \frac{3}{13} \cdot - 39$ .

Cancel the common factor of $13$ .

Move the leading negative in $- \frac{3}{13}$ into the numerator.

$n = \frac{- 3}{13} \cdot - 39$

Factor $13$ out of $- 39$ .

$n = \frac{- 3}{13} \cdot (13 (- 3))$

Cancel the common factor.

$n = \frac{- 3}{13} \cdot (13 \cdot - 3)$

Rewrite the expression.

$n = - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$n = 9$

Solve for n 2/3(n-6)=5n-43

Related Questions

Support LCMGCF.com by disabling your adblocker.