w^2+w+w=120

Solution for w^2+w+w=120 equation:

Simplifying
w2 + w + w = 120

Reorder the terms:
w + w + w2 = 120

Combine like terms: w + w = 2w
2w + w2 = 120

Solving
2w + w2 = 120

Solving for variable 'w'.

Reorder the terms:
-120 + 2w + w2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 2w + w2 = 0

Factor a trinomial.
(-12 + -1w)(10 + -1w) = 0

Subproblem 1
Set the factor '(-12 + -1w)' equal to zero and attempt to solve:

Simplifying
-12 + -1w = 0

Solving
-12 + -1w = 0

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

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

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

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

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

Simplifying
w = -12
Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve:

Simplifying
10 + -1w = 0

Solving
10 + -1w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1w = 0 + -10
-1w = 0 + -10

Combine like terms: 0 + -10 = -10
-1w = -10

Divide each side by '-1'.
w = 10

Simplifying
w = 10
Solution
w = {-12, 10}