2x-3=x^2-6

Solution for 2x-3=x^2-6 equation:

Simplifying
2x + -3 = x2 + -6

Reorder the terms:
-3 + 2x = x2 + -6

Reorder the terms:
-3 + 2x = -6 + x2

Solving
-3 + 2x = -6 + x2

Solving for variable 'x'.

Reorder the terms:
-3 + 6 + 2x + -1x2 = -6 + x2 + 6 + -1x2

Combine like terms: -3 + 6 = 3
3 + 2x + -1x2 = -6 + x2 + 6 + -1x2

Reorder the terms:
3 + 2x + -1x2 = -6 + 6 + x2 + -1x2

Combine like terms: -6 + 6 = 0
3 + 2x + -1x2 = 0 + x2 + -1x2
3 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + 2x + -1x2 = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {3, -1}