Solve for y 8(2y+5)=12y-(2y+14)

$8 (2 y + 5) = 12 y - (2 y + 14)$

Step 1

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$12 y - (2 y + 14) = 8 (2 y + 5)$

Step 2

Simplify $12 y - (2 y + 14)$ .

Simplify each term.

Apply the distributive property.

$12 y - (2 y) - 1 \cdot 14 = 8 (2 y + 5)$

Multiply $2$ by $- 1$ .

$12 y - 2 y - 1 \cdot 14 = 8 (2 y + 5)$

Multiply $- 1$ by $14$ .

$12 y - 2 y - 14 = 8 (2 y + 5)$

Subtract $2 y$ from $12 y$ .

$10 y - 14 = 8 (2 y + 5)$

Step 3

Simplify $8 (2 y + 5)$ .

Apply the distributive property.

$10 y - 14 = 8 (2 y) + 8 \cdot 5$

Multiply.

Multiply $2$ by $8$ .

$10 y - 14 = 16 y + 8 \cdot 5$

Multiply $8$ by $5$ .

$10 y - 14 = 16 y + 40$

Step 4

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

Subtract $16 y$ from both sides of the equation.

$10 y - 14 - 16 y = 40$

Subtract $16 y$ from $10 y$ .

$- 6 y - 14 = 40$

Step 5

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

Add $14$ to both sides of the equation.

$- 6 y = 40 + 14$

Add $40$ and $14$ .

$- 6 y = 54$

Step 6

Divide each term in $- 6 y = 54$ by $- 6$ and simplify.

Divide each term in $- 6 y = 54$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{54}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{54}{- 6}$

Divide $y$ by $1$ .

$y = \frac{54}{- 6}$

Simplify the right side.

Divide $54$ by $- 6$ .

$y = - 9$

Solve for y 8(2y+5)=12y-(2y+14)

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