2w^2+4w-96=0

Solution for 2w^2+4w-96=0 equation:

Simplifying
2w2 + 4w + -96 = 0

Reorder the terms:
-96 + 4w + 2w2 = 0

Solving
-96 + 4w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-48 + 2w + w2) = 0

Factor a trinomial.
2((-8 + -1w)(6 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -1w)' equal to zero and attempt to solve:

Simplifying
-8 + -1w = 0

Solving
-8 + -1w = 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 + -1w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1w = 0 + 8
-1w = 0 + 8

Combine like terms: 0 + 8 = 8
-1w = 8

Divide each side by '-1'.
w = -8

Simplifying
w = -8
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

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