Solve for y 0.5(2y-1)-(0.5-0.2y)+1=0

$0.5 (2 y - 1) - (0.5 - 0.2 y) + 1 = 0$

Simplify $0.5 (2 y - 1) - (0.5 - 0.2 y) + 1$ .

Simplify each term.

Apply the distributive property.

$0.5 (2 y) + 0.5 \cdot - 1 - (0.5 - 0.2 y) + 1 = 0$

Multiply $0.5 (2 y)$ .

Multiply $2$ by $0.5$ .

$1 y + 0.5 \cdot - 1 - (0.5 - 0.2 y) + 1 = 0$

Multiply $y$ by $1$ .

$y + 0.5 \cdot - 1 - (0.5 - 0.2 y) + 1 = 0$

Multiply $0.5$ by $- 1$ .

$y - 0.5 - (0.5 - 0.2 y) + 1 = 0$

Apply the distributive property.

$y - 0.5 - 1 \cdot 0.5 - (- 0.2 y) + 1 = 0$

Multiply $- 1$ by $0.5$ .

$y - 0.5 - 0.5 - (- 0.2 y) + 1 = 0$

Multiply $- 0.2$ by $- 1$ .

$y - 0.5 - 0.5 + 0.2 y + 1 = 0$

Simplify by adding terms.

Add $y$ and $0.2 y$ .

$1.2 y - 0.5 - 0.5 + 1 = 0$

Simplify by adding and subtracting.

Subtract $0.5$ from $- 0.5$ .

$1.2 y - 1 + 1 = 0$

Add $- 1$ and $1$ .

$1.2 y + 0 = 0$

Add $1.2 y$ and $0$ .

$1.2 y = 0$

Divide each term in $1.2 y = 0$ by $1.2$ and simplify.

Divide each term in $1.2 y = 0$ by $1.2$ .

$\frac{1.2 y}{1.2} = \frac{0}{1.2}$

Simplify the left side.

Cancel the common factor of $1.2$ .

Cancel the common factor.

$\frac{1.2 y}{1.2} = \frac{0}{1.2}$

Divide $y$ by $1$ .

$y = \frac{0}{1.2}$

Simplify the right side.

Divide $0$ by $1.2$ .

$y = 0$