x(x-1)=x+15

Solution for x(x-1)=x+15 equation:

Simplifying
x(x + -1) = x + 15

Reorder the terms:
x(-1 + x) = x + 15
(-1 * x + x * x) = x + 15
(-1x + x2) = x + 15

Reorder the terms:
-1x + x2 = 15 + x

Solving
-1x + x2 = 15 + x

Solving for variable 'x'.

Reorder the terms:
-15 + -1x + -1x + x2 = 15 + x + -15 + -1x

Combine like terms: -1x + -1x = -2x
-15 + -2x + x2 = 15 + x + -15 + -1x

Reorder the terms:
-15 + -2x + x2 = 15 + -15 + x + -1x

Combine like terms: 15 + -15 = 0
-15 + -2x + x2 = 0 + x + -1x
-15 + -2x + x2 = x + -1x

Combine like terms: x + -1x = 0
-15 + -2x + x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-3, 5}