15-x^2=x^2-x

Solution for 15-x^2=x^2-x equation:

Simplifying
15 + -1x2 = x2 + -1x

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

Solving
15 + -1x2 = -1x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(3 + -1x)(5 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {3, -2.5}