w^2+15w=-54

Solution for w^2+15w=-54 equation:

Simplifying
w2 + 15w = -54

Reorder the terms:
15w + w2 = -54

Solving
15w + w2 = -54

Solving for variable 'w'.

Reorder the terms:
54 + 15w + w2 = -54 + 54

Combine like terms: -54 + 54 = 0
54 + 15w + w2 = 0

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

Subproblem 1
Set the factor '(9 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

Solving
9 + w = 0

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

Add '-9' to each side of the equation.
9 + -9 + w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + w = 0 + -9
w = 0 + -9

Combine like terms: 0 + -9 = -9
w = -9

Simplifying
w = -9
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 = {-9, -6}