(3y+6)2=36

Take the square root of each side of the equation to set up the solution for y

(3y+6)2⋅12=±36

Remove the perfect root factor 3y+6 under the radical to solve for y.

3y+6=±36

Rewrite 36 as 62.

3y+6=±62

Pull terms out from under the radical, assuming positive real numbers.

3y+6=±6

3y+6=±6

First, use the positive value of the ± to find the first solution.

3y+6=6

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

Subtract 6 from both sides of the equation.

3y=6-6

Subtract 6 from 6.

3y=0

3y=0

Divide each term by 3 and simplify.

Divide each term in 3y=0 by 3.

3y3=03

Cancel the common factor of 3.

Cancel the common factor.

3y3=03

Divide y by 1.

y=03

y=03

Divide 0 by 3.

y=0

y=0

Next, use the negative value of the ± to find the second solution.

3y+6=-6

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

Subtract 6 from both sides of the equation.

3y=-6-6

Subtract 6 from -6.

3y=-12

3y=-12

Divide each term by 3 and simplify.

Divide each term in 3y=-12 by 3.

3y3=-123

Cancel the common factor of 3.

Cancel the common factor.

3y3=-123

Divide y by 1.

y=-123

y=-123

Divide -12 by 3.

y=-4

y=-4

The complete solution is the result of both the positive and negative portions of the solution.

y=0,-4

y=0,-4

Solve for y (3y+6)^2=36