w^2=-8-6w

Solution for w^2=-8-6w equation:

Simplifying
w2 = -8 + -6w

Solving
w2 = -8 + -6w

Solving for variable 'w'.

Reorder the terms:
8 + 6w + w2 = -8 + -6w + 8 + 6w

Reorder the terms:
8 + 6w + w2 = -8 + 8 + -6w + 6w

Combine like terms: -8 + 8 = 0
8 + 6w + w2 = 0 + -6w + 6w
8 + 6w + w2 = -6w + 6w

Combine like terms: -6w + 6w = 0
8 + 6w + w2 = 0

Factor a trinomial.
(4 + w)(2 + w) = 0

Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

Add '-4' to each side of the equation.
4 + -4 + w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + w = 0 + -4
w = 0 + -4

Combine like terms: 0 + -4 = -4
w = -4

Simplifying
w = -4
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

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

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

Simplifying
w = -2
Solution
w = {-4, -2}