w^2+12w=-35

Solution for w^2+12w=-35 equation:

Simplifying
w2 + 12w = -35

Reorder the terms:
12w + w2 = -35

Solving
12w + w2 = -35

Solving for variable 'w'.

Reorder the terms:
35 + 12w + w2 = -35 + 35

Combine like terms: -35 + 35 = 0
35 + 12w + w2 = 0

Factor a trinomial.
(7 + w)(5 + w) = 0

Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

Solving
7 + w = 0

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

Add '-7' to each side of the equation.
7 + -7 + w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + w = 0 + -7
w = 0 + -7

Combine like terms: 0 + -7 = -7
w = -7

Simplifying
w = -7
Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

Add '-5' to each side of the equation.
5 + -5 + w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + w = 0 + -5
w = 0 + -5

Combine like terms: 0 + -5 = -5
w = -5

Simplifying
w = -5
Solution
w = {-7, -5}