x-4=x^2-6

Solution for x-4=x^2-6 equation:

Simplifying
x + -4 = x2 + -6

Reorder the terms:
-4 + x = x2 + -6

Reorder the terms:
-4 + x = -6 + x2

Solving
-4 + x = -6 + x2

Solving for variable 'x'.

Reorder the terms:
-4 + 6 + x + -1x2 = -6 + x2 + 6 + -1x2

Combine like terms: -4 + 6 = 2
2 + x + -1x2 = -6 + x2 + 6 + -1x2

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

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

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

Factor a trinomial.
(2 + -1x)(1 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, -1}