(y+9)(y+9)=144

Solution for (y+9)(y+9)=144 equation:

Simplifying
(y + 9)(y + 9) = 144

Reorder the terms:
(9 + y)(y + 9) = 144

Reorder the terms:
(9 + y)(9 + y) = 144

Multiply (9 + y) * (9 + y)
(9(9 + y) + y(9 + y)) = 144
((9 * 9 + y * 9) + y(9 + y)) = 144
((81 + 9y) + y(9 + y)) = 144
(81 + 9y + (9 * y + y * y)) = 144
(81 + 9y + (9y + y2)) = 144

Combine like terms: 9y + 9y = 18y
(81 + 18y + y2) = 144

Solving
81 + 18y + y2 = 144

Solving for variable 'y'.

Reorder the terms:
81 + -144 + 18y + y2 = 144 + -144

Combine like terms: 81 + -144 = -63
-63 + 18y + y2 = 144 + -144

Combine like terms: 144 + -144 = 0
-63 + 18y + y2 = 0

Factor a trinomial.
(-21 + -1y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-21 + -1y)' equal to zero and attempt to solve:

Simplifying
-21 + -1y = 0

Solving
-21 + -1y = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1y = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1y = 0 + 21
-1y = 0 + 21

Combine like terms: 0 + 21 = 21
-1y = 21

Divide each side by '-1'.
y = -21

Simplifying
y = -21
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 = {-21, 3}