6-4x=x^2-6

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

Simplifying
6 + -4x = x2 + -6

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

Solving
6 + -4x = -6 + x2

Solving for variable 'x'.

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

Combine like terms: 6 + 6 = 12
12 + -4x + -1x2 = -6 + x2 + 6 + -1x2

Reorder the terms:
12 + -4x + -1x2 = -6 + 6 + x2 + -1x2

Combine like terms: -6 + 6 = 0
12 + -4x + -1x2 = 0 + x2 + -1x2
12 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -4x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(6 + 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {2, -6}