256=x(24+x)

Solution for 256=x(24+x) equation:

Simplifying
256 = x(24 + x)
256 = (24 * x + x * x)
256 = (24x + x2)

Solving
256 = 24x + x2

Solving for variable 'x'.

Reorder the terms:
256 + -24x + -1x2 = 24x + -24x + x2 + -1x2

Combine like terms: 24x + -24x = 0
256 + -24x + -1x2 = 0 + x2 + -1x2
256 + -24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
256 + -24x + -1x2 = 0

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

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

Simplifying
32 + x = 0

Solving
32 + x = 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 + x = 0 + -32

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

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

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