4w^2+5=-12w

Solution for 4w^2+5=-12w equation:

Simplifying
4w2 + 5 = -12w

Reorder the terms:
5 + 4w2 = -12w

Solving
5 + 4w2 = -12w

Solving for variable 'w'.

Reorder the terms:
5 + 12w + 4w2 = -12w + 12w

Combine like terms: -12w + 12w = 0
5 + 12w + 4w2 = 0

Factor a trinomial.
(5 + 2w)(1 + 2w) = 0

Subproblem 1
Set the factor '(5 + 2w)' equal to zero and attempt to solve:

Simplifying
5 + 2w = 0

Solving
5 + 2w = 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 + 2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2w = 0 + -5
2w = 0 + -5

Combine like terms: 0 + -5 = -5
2w = -5

Divide each side by '2'.
w = -2.5

Simplifying
w = -2.5
Subproblem 2
Set the factor '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {-2.5, -0.5}