Solve for y -2(y+6)+6y=4(y-3)

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

Step 1

Simplify $- 2 (y + 6) + 6 y$ .

Simplify each term.

Apply the distributive property.

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

Multiply $- 2$ by $6$ .

$- 2 y - 12 + 6 y = 4 (y - 3)$

Add $- 2 y$ and $6 y$ .

$4 y - 12 = 4 (y - 3)$

Step 2

Simplify $4 (y - 3)$ .

Apply the distributive property.

$4 y - 12 = 4 y + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$4 y - 12 = 4 y - 12$

Step 3

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

Subtract $4 y$ from both sides of the equation.

$4 y - 12 - 4 y = - 12$

Combine the opposite terms in $4 y - 12 - 4 y$ .

Subtract $4 y$ from $4 y$ .

$0 - 12 = - 12$

Subtract $12$ from $0$ .

$- 12 = - 12$

Step 4

Since $- 12 = - 12$ , the equation will always be true for any value of $y$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$