4w(20w-56)=-128

Solution for 4w(20w-56)=-128 equation:

Simplifying
4w(20w + -56) = -128

Reorder the terms:
4w(-56 + 20w) = -128
(-56 * 4w + 20w * 4w) = -128
(-224w + 80w2) = -128

Solving
-224w + 80w2 = -128

Solving for variable 'w'.

Reorder the terms:
128 + -224w + 80w2 = -128 + 128

Combine like terms: -128 + 128 = 0
128 + -224w + 80w2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(8 + -14w + 5w2) = 0

Factor a trinomial.
16((4 + -5w)(2 + -1w)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(4 + -5w)' equal to zero and attempt to solve:

Simplifying
4 + -5w = 0

Solving
4 + -5w = 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 + -5w = 0 + -4

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

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

Divide each side by '-5'.
w = 0.8

Simplifying
w = 0.8
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {0.8, 2}