Solve for y 6(y-1/3)=4(3y-5)

$6 (y - \frac{1}{3}) = 4 (3 y - 5)$

Simplify $6 (y - \frac{1}{3})$ .

Start simplifying.

$0 + 0 + 6 (y - \frac{1}{3}) = 4 (3 y - 5)$

Simplify by adding zeros.

$6 (y - \frac{1}{3}) = 4 (3 y - 5)$

Apply the distributive property.

$6 y + 6 (- \frac{1}{3}) = 4 (3 y - 5)$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$6 y + 6 (\frac{- 1}{3}) = 4 (3 y - 5)$

Factor $3$ out of $6$ .

$6 y + 3 (2) \frac{- 1}{3} = 4 (3 y - 5)$

Cancel the common factor.

$6 y + 3 \cdot 2 \frac{- 1}{3} = 4 (3 y - 5)$

Rewrite the expression.

$6 y + 2 \cdot - 1 = 4 (3 y - 5)$

Multiply $2$ by $- 1$ .

$6 y - 2 = 4 (3 y - 5)$

Simplify $4 (3 y - 5)$ .

Apply the distributive property.

$6 y - 2 = 4 (3 y) + 4 \cdot - 5$

Multiply.

Multiply $3$ by $4$ .

$6 y - 2 = 12 y + 4 \cdot - 5$

Multiply $4$ by $- 5$ .

$6 y - 2 = 12 y - 20$

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

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

$6 y - 2 - 12 y = - 20$

Subtract $12 y$ from $6 y$ .

$- 6 y - 2 = - 20$

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

Add $2$ to both sides of the equation.

$- 6 y = - 20 + 2$

Add $- 20$ and $2$ .

$- 6 y = - 18$

Divide each term in $- 6 y = - 18$ by $- 6$ and simplify.

Divide each term in $- 6 y = - 18$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 18}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 18}{- 6}$

Divide $y$ by $1$ .

$y = \frac{- 18}{- 6}$

Simplify the right side.

Divide $- 18$ by $- 6$ .

$y = 3$

Solve for y 6(y-1/3)=4(3y-5)

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