x(x+6)=x+24

Solution for x(x+6)=x+24 equation:

Simplifying
x(x + 6) = x + 24

Reorder the terms:
x(6 + x) = x + 24
(6 * x + x * x) = x + 24
(6x + x2) = x + 24

Reorder the terms:
6x + x2 = 24 + x

Solving
6x + x2 = 24 + x

Solving for variable 'x'.

Reorder the terms:
-24 + 6x + -1x + x2 = 24 + x + -24 + -1x

Combine like terms: 6x + -1x = 5x
-24 + 5x + x2 = 24 + x + -24 + -1x

Reorder the terms:
-24 + 5x + x2 = 24 + -24 + x + -1x

Combine like terms: 24 + -24 = 0
-24 + 5x + x2 = 0 + x + -1x
-24 + 5x + x2 = x + -1x

Combine like terms: x + -1x = 0
-24 + 5x + x2 = 0

Factor a trinomial.
(-8 + -1x)(3 + -1x) = 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-8, 3}