w^2+21w+90=0

Solution for w^2+21w+90=0 equation:

Simplifying
w2 + 21w + 90 = 0

Reorder the terms:
90 + 21w + w2 = 0

Solving
90 + 21w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(15 + w)(6 + w) = 0

Subproblem 1
Set the factor '(15 + w)' equal to zero and attempt to solve:

Simplifying
15 + w = 0

Solving
15 + w = 0

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

Add '-15' to each side of the equation.
15 + -15 + w = 0 + -15

Combine like terms: 15 + -15 = 0
0 + w = 0 + -15
w = 0 + -15

Combine like terms: 0 + -15 = -15
w = -15

Simplifying
w = -15
Subproblem 2
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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 = 0 + -6

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

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

Simplifying
w = -6
Solution
w = {-15, -6}