Solve for y 5(y-4)=7(2y+1)

$5 (y - 4) = 7 (2 y + 1)$

Step 1

Simplify $5 (y - 4)$ .

Rewrite.

$0 + 0 + 5 (y - 4) = 7 (2 y + 1)$

Simplify by adding zeros.

$5 (y - 4) = 7 (2 y + 1)$

Apply the distributive property.

$5 y + 5 \cdot - 4 = 7 (2 y + 1)$

Multiply $5$ by $- 4$ .

$5 y - 20 = 7 (2 y + 1)$

Step 2

Simplify $7 (2 y + 1)$ .

Apply the distributive property.

$5 y - 20 = 7 (2 y) + 7 \cdot 1$

Multiply.

Multiply $2$ by $7$ .

$5 y - 20 = 14 y + 7 \cdot 1$

Multiply $7$ by $1$ .

$5 y - 20 = 14 y + 7$

Step 3

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

Subtract $14 y$ from both sides of the equation.

$5 y - 20 - 14 y = 7$

Subtract $14 y$ from $5 y$ .

$- 9 y - 20 = 7$

Step 4

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

Add $20$ to both sides of the equation.

$- 9 y = 7 + 20$

Add $7$ and $20$ .

$- 9 y = 27$

Step 5

Divide each term in $- 9 y = 27$ by $- 9$ and simplify.

Divide each term in $- 9 y = 27$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{27}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{27}{- 9}$

Divide $y$ by $1$ .

$y = \frac{27}{- 9}$

Simplify the right side.

Divide $27$ by $- 9$ .

$y = - 3$