X^2+6=12-X

Solution for X^2+6=12-X equation:

Simplifying
X2 + 6 = 12 + -1X

Reorder the terms:
6 + X2 = 12 + -1X

Solving
6 + X2 = 12 + -1X

Solving for variable 'X'.

Reorder the terms:
6 + -12 + X + X2 = 12 + -1X + -12 + X

Combine like terms: 6 + -12 = -6
-6 + X + X2 = 12 + -1X + -12 + X

Reorder the terms:
-6 + X + X2 = 12 + -12 + -1X + X

Combine like terms: 12 + -12 = 0
-6 + X + X2 = 0 + -1X + X
-6 + X + X2 = -1X + X

Combine like terms: -1X + X = 0
-6 + X + X2 = 0

Factor a trinomial.
(-3 + -1X)(2 + -1X) = 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 '(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
Solution
X = {-3, 2}