w^2=-48-14w

Solution for w^2=-48-14w equation:

Simplifying
w2 = -48 + -14w

Solving
w2 = -48 + -14w

Solving for variable 'w'.

Reorder the terms:
48 + 14w + w2 = -48 + -14w + 48 + 14w

Reorder the terms:
48 + 14w + w2 = -48 + 48 + -14w + 14w

Combine like terms: -48 + 48 = 0
48 + 14w + w2 = 0 + -14w + 14w
48 + 14w + w2 = -14w + 14w

Combine like terms: -14w + 14w = 0
48 + 14w + w2 = 0

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

Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

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

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

Simplifying
w = -8
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 = {-8, -6}