x^2-13x+24=x

Solution for x^2-13x+24=x equation:

Simplifying
x2 + -13x + 24 = x

Reorder the terms:
24 + -13x + x2 = x

Solving
24 + -13x + x2 = x

Solving for variable 'x'.

Reorder the terms:
24 + -13x + -1x + x2 = x + -1x

Combine like terms: -13x + -1x = -14x
24 + -14x + x2 = x + -1x

Combine like terms: x + -1x = 0
24 + -14x + x2 = 0

Factor a trinomial.
(2 + -1x)(12 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {2, 12}