x+15=x(x-1)

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

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

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

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

Solving
15 + x = -1x + x2

Solving for variable 'x'.

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

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

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

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

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

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