x^2=x+72

Solution for x^2=x+72 equation:

Simplifying
x2 = x + 72

Reorder the terms:
x2 = 72 + x

Solving
x2 = 72 + x

Solving for variable 'x'.

Reorder the terms:
-72 + -1x + x2 = 72 + x + -72 + -1x

Reorder the terms:
-72 + -1x + x2 = 72 + -72 + x + -1x

Combine like terms: 72 + -72 = 0
-72 + -1x + x2 = 0 + x + -1x
-72 + -1x + x2 = x + -1x

Combine like terms: x + -1x = 0
-72 + -1x + x2 = 0

Factor a trinomial.
(-8 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-8, 9}