w^2+13w=-42

Solution for w^2+13w=-42 equation:

Simplifying
w2 + 13w = -42

Reorder the terms:
13w + w2 = -42

Solving
13w + w2 = -42

Solving for variable 'w'.

Reorder the terms:
42 + 13w + w2 = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 13w + w2 = 0

Factor a trinomial.
(7 + w)(6 + 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 '(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 = {-7, -6}