(2y+9)(2y+9)=225

Solution for (2y+9)(2y+9)=225 equation:

Simplifying
(2y + 9)(2y + 9) = 225

Reorder the terms:
(9 + 2y)(2y + 9) = 225

Reorder the terms:
(9 + 2y)(9 + 2y) = 225

Multiply (9 + 2y) * (9 + 2y)
(9(9 + 2y) + 2y * (9 + 2y)) = 225
((9 * 9 + 2y * 9) + 2y * (9 + 2y)) = 225
((81 + 18y) + 2y * (9 + 2y)) = 225
(81 + 18y + (9 * 2y + 2y * 2y)) = 225
(81 + 18y + (18y + 4y2)) = 225

Combine like terms: 18y + 18y = 36y
(81 + 36y + 4y2) = 225

Solving
81 + 36y + 4y2 = 225

Solving for variable 'y'.

Reorder the terms:
81 + -225 + 36y + 4y2 = 225 + -225

Combine like terms: 81 + -225 = -144
-144 + 36y + 4y2 = 225 + -225

Combine like terms: 225 + -225 = 0
-144 + 36y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-36 + 9y + y2) = 0

Factor a trinomial.
4((-12 + -1y)(3 + -1y)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-12 + -1y)' equal to zero and attempt to solve:

Simplifying
-12 + -1y = 0

Solving
-12 + -1y = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1y = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1y = 0 + 12
-1y = 0 + 12

Combine like terms: 0 + 12 = 12
-1y = 12

Divide each side by '-1'.
y = -12

Simplifying
y = -12
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 = {-12, 3}