Solve for y 7(1-y)=-3(y-2)

$7 (1 - y) = - 3 (y - 2)$

Simplify $7 (1 - y)$ .

Start simplifying.

$0 + 0 + 7 (1 - y) = - 3 (y - 2)$

Simplify by adding zeros.

$7 (1 - y) = - 3 (y - 2)$

Apply the distributive property.

$7 \cdot 1 + 7 (- y) = - 3 (y - 2)$

Multiply.

Multiply $7$ by $1$ .

$7 + 7 (- y) = - 3 (y - 2)$

Multiply $- 1$ by $7$ .

$7 - 7 y = - 3 (y - 2)$

Simplify $- 3 (y - 2)$ .

Apply the distributive property.

$7 - 7 y = - 3 y - 3 \cdot - 2$

Multiply $- 3$ by $- 2$ .

$7 - 7 y = - 3 y + 6$

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

Add $3 y$ to both sides of the equation.

$7 - 7 y + 3 y = 6$

Add $- 7 y$ and $3 y$ .

$7 - 4 y = 6$

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

Subtract $7$ from both sides of the equation.

$- 4 y = 6 - 7$

Subtract $7$ from $6$ .

$- 4 y = - 1$

Divide each term in $- 4 y = - 1$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 1$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 1}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 1}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 1}{- 4}$

Simplify the right side.

Dividing two negative values results in a positive value.

$y = \frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{1}{4}$

Decimal Form:

$y = 0.25$