4w^2+16w=128

Solution for 4w^2+16w=128 equation:

Simplifying
4w2 + 16w = 128

Reorder the terms:
16w + 4w2 = 128

Solving
16w + 4w2 = 128

Solving for variable 'w'.

Reorder the terms:
-128 + 16w + 4w2 = 128 + -128

Combine like terms: 128 + -128 = 0
-128 + 16w + 4w2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-32 + 4w + w2) = 0

Factor a trinomial.
4((-8 + -1w)(4 + -1w)) = 0

Ignore the factor 4.
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 '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 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 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-8, 4}