-16x^2+128x=256

Solution for -16x^2+128x=256 equation:

Simplifying
-16x2 + 128x = 256

Reorder the terms:
128x + -16x2 = 256

Solving
128x + -16x2 = 256

Solving for variable 'x'.

Reorder the terms:
-256 + 128x + -16x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 128x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-16 + 8x + -1x2) = 0

Factor a trinomial.
16((-4 + x)(4 + -1x)) = 0

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

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

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

Simplifying
x = 4
Solution
x = {4, 4}