24x+x^2=256

Solution for 24x+x^2=256 equation:

Simplifying
24x + x2 = 256

Solving
24x + x2 = 256

Solving for variable 'x'.

Reorder the terms:
-256 + 24x + x2 = 256 + -256

Combine like terms: 256 + -256 = 0
-256 + 24x + x2 = 0

Factor a trinomial.
(-32 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-32 + -1x)' equal to zero and attempt to solve:

Simplifying
-32 + -1x = 0

Solving
-32 + -1x = 0

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

Add '32' to each side of the equation.
-32 + 32 + -1x = 0 + 32

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

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

Divide each side by '-1'.
x = -32

Simplifying
x = -32
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

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

Simplifying
x = 8
Solution
x = {-32, 8}