Solve for y 6(2y+6)=4(9+3y)

$6 (2 y + 6) = 4 (9 + 3 y)$

Step 1

Simplify $6 (2 y + 6)$ .

Rewrite.

$0 + 0 + 6 (2 y + 6) = 4 (9 + 3 y)$

Simplify by adding zeros.

$6 (2 y + 6) = 4 (9 + 3 y)$

Apply the distributive property.

$6 (2 y) + 6 \cdot 6 = 4 (9 + 3 y)$

Multiply.

Multiply $2$ by $6$ .

$12 y + 6 \cdot 6 = 4 (9 + 3 y)$

Multiply $6$ by $6$ .

$12 y + 36 = 4 (9 + 3 y)$

Step 2

Simplify $4 (9 + 3 y)$ .

Apply the distributive property.

$12 y + 36 = 4 \cdot 9 + 4 (3 y)$

Multiply.

Multiply $4$ by $9$ .

$12 y + 36 = 36 + 4 (3 y)$

Multiply $3$ by $4$ .

$12 y + 36 = 36 + 12 y$

Step 3

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

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

$12 y + 36 - 12 y = 36$

Combine the opposite terms in $12 y + 36 - 12 y$ .

Subtract $12 y$ from $12 y$ .

$0 + 36 = 36$

Add $0$ and $36$ .

$36 = 36$

Step 4

Since $36 = 36$ , 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:

$(- \infty, \infty)$