32x-256=x^2

Solution for 32x-256=x^2 equation:

Simplifying
32x + -256 = x2

Reorder the terms:
-256 + 32x = x2

Solving
-256 + 32x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
-256 + 32x + -1x2 = 0

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

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

Simplifying
-16 + x = 0

Solving
-16 + x = 0

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

Add '16' to each side of the equation.
-16 + 16 + x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + x = 0 + 16
x = 0 + 16

Combine like terms: 0 + 16 = 16
x = 16

Simplifying
x = 16
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {16, 16}