(12+w)(w)=120

Solution for (12+w)(w)=120 equation:

Simplifying
(12 + w)(w) = 120

Reorder the terms for easier multiplication:
w(12 + w) = 120
(12 * w + w * w) = 120
(12w + w2) = 120

Solving
12w + w2 = 120

Solving for variable 'w'.

Reorder the terms:
-120 + 12w + w2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 12w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 12w + 120 + w2 = 0 + 120

Reorder the terms:
-120 + 120 + 12w + w2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 12w + w2 = 0 + 120
12w + w2 = 0 + 120

Combine like terms: 0 + 120 = 120
12w + w2 = 120

The w term is 12w.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12w + 36 + w2 = 120 + 36

Reorder the terms:
36 + 12w + w2 = 120 + 36

Combine like terms: 120 + 36 = 156
36 + 12w + w2 = 156

Factor a perfect square on the left side:
(w + 6)(w + 6) = 156

Calculate the square root of the right side: 12.489995997

Break this problem into two subproblems by setting 
(w + 6) equal to 12.489995997 and -12.489995997.

Subproblem 1
w + 6 = 12.489995997

Simplifying
w + 6 = 12.489995997

Reorder the terms:
6 + w = 12.489995997

Solving
6 + w = 12.489995997

Solving for variable 'w'.

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

Add '-6' to each side of the equation.
6 + -6 + w = 12.489995997 + -6

Combine like terms: 6 + -6 = 0
0 + w = 12.489995997 + -6
w = 12.489995997 + -6

Combine like terms: 12.489995997 + -6 = 6.489995997
w = 6.489995997

Simplifying
w = 6.489995997

Subproblem 2
w + 6 = -12.489995997

Simplifying
w + 6 = -12.489995997

Reorder the terms:
6 + w = -12.489995997

Solving
6 + w = -12.489995997

Solving for variable 'w'.

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

Add '-6' to each side of the equation.
6 + -6 + w = -12.489995997 + -6

Combine like terms: 6 + -6 = 0
0 + w = -12.489995997 + -6
w = -12.489995997 + -6

Combine like terms: -12.489995997 + -6 = -18.489995997
w = -18.489995997

Simplifying
w = -18.489995997

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {6.489995997, -18.489995997}