(y+3)(y+3)-36=0

Solution for (y+3)(y+3)-36=0 equation:

Simplifying
(y + 3)(y + 3) + -36 = 0

Reorder the terms:
(3 + y)(y + 3) + -36 = 0

Reorder the terms:
(3 + y)(3 + y) + -36 = 0

Multiply (3 + y) * (3 + y)
(3(3 + y) + y(3 + y)) + -36 = 0
((3 * 3 + y * 3) + y(3 + y)) + -36 = 0
((9 + 3y) + y(3 + y)) + -36 = 0
(9 + 3y + (3 * y + y * y)) + -36 = 0
(9 + 3y + (3y + y2)) + -36 = 0

Combine like terms: 3y + 3y = 6y
(9 + 6y + y2) + -36 = 0

Reorder the terms:
9 + -36 + 6y + y2 = 0

Combine like terms: 9 + -36 = -27
-27 + 6y + y2 = 0

Solving
-27 + 6y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-9 + -1y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-9 + -1y)' equal to zero and attempt to solve:

Simplifying
-9 + -1y = 0

Solving
-9 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + -1y = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1y = 0 + 9
-1y = 0 + 9

Combine like terms: 0 + 9 = 9
-1y = 9

Divide each side by '-1'.
y = -9

Simplifying
y = -9
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-9, 3}