(w+9)(w+9)=144

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

Simplifying
(w + 9)(w + 9) = 144

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

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

Multiply (9 + w) * (9 + w)
(9(9 + w) + w(9 + w)) = 144
((9 * 9 + w * 9) + w(9 + w)) = 144
((81 + 9w) + w(9 + w)) = 144
(81 + 9w + (9 * w + w * w)) = 144
(81 + 9w + (9w + w2)) = 144

Combine like terms: 9w + 9w = 18w
(81 + 18w + w2) = 144

Solving
81 + 18w + w2 = 144

Solving for variable 'w'.

Reorder the terms:
81 + -144 + 18w + w2 = 144 + -144

Combine like terms: 81 + -144 = -63
-63 + 18w + w2 = 144 + -144

Combine like terms: 144 + -144 = 0
-63 + 18w + w2 = 0

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

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

Simplifying
-21 + -1w = 0

Solving
-21 + -1w = 0

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

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

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

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

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

Simplifying
w = -21
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

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

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

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

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

Simplifying
w = 3
Solution
w = {-21, 3}