Solve for y 2(3y-4)=3(y-2/3)

$2 (3 y - 4) = 3 (y - \frac{2}{3})$

Step 1

Simplify $2 (3 y - 4)$ .

Rewrite.

$0 + 0 + 2 (3 y - 4) = 3 (y - \frac{2}{3})$

Simplify by adding zeros.

$2 (3 y - 4) = 3 (y - \frac{2}{3})$

Apply the distributive property.

$2 (3 y) + 2 \cdot - 4 = 3 (y - \frac{2}{3})$

Multiply.

Multiply $3$ by $2$ .

$6 y + 2 \cdot - 4 = 3 (y - \frac{2}{3})$

Multiply $2$ by $- 4$ .

$6 y - 8 = 3 (y - \frac{2}{3})$

Step 2

Simplify $3 (y - \frac{2}{3})$ .

Apply the distributive property.

$6 y - 8 = 3 y + 3 (- \frac{2}{3})$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$6 y - 8 = 3 y + 3 (\frac{- 2}{3})$

Cancel the common factor.

$6 y - 8 = 3 y + 3 (\frac{- 2}{3})$

Rewrite the expression.

$6 y - 8 = 3 y - 2$

Step 3

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

Subtract $3 y$ from both sides of the equation.

$6 y - 8 - 3 y = - 2$

Subtract $3 y$ from $6 y$ .

$3 y - 8 = - 2$

Step 4

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

Add $8$ to both sides of the equation.

$3 y = - 2 + 8$

Add $- 2$ and $8$ .

$3 y = 6$

Step 5

Divide each term in $3 y = 6$ by $3$ and simplify.

Divide each term in $3 y = 6$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3}$

Divide $y$ by $1$ .

$y = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$y = 2$

Solve for y 2(3y-4)=3(y-2/3)

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