24=x(2+x)

Solution for 24=x(2+x) equation:

Simplifying
24 = x(2 + x)
24 = (2 * x + x * x)
24 = (2x + x2)

Solving
24 = 2x + x2

Solving for variable 'x'.

Reorder the terms:
24 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
24 + -2x + -1x2 = 0 + x2 + -1x2
24 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + -2x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(6 + x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {4, -6}