14x-12=36+x^2

Solution for 14x-12=36+x^2 equation:

Simplifying
14x + -12 = 36 + x2

Reorder the terms:
-12 + 14x = 36 + x2

Solving
-12 + 14x = 36 + x2

Solving for variable 'x'.

Reorder the terms:
-12 + -36 + 14x + -1x2 = 36 + x2 + -36 + -1x2

Combine like terms: -12 + -36 = -48
-48 + 14x + -1x2 = 36 + x2 + -36 + -1x2

Reorder the terms:
-48 + 14x + -1x2 = 36 + -36 + x2 + -1x2

Combine like terms: 36 + -36 = 0
-48 + 14x + -1x2 = 0 + x2 + -1x2
-48 + 14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-48 + 14x + -1x2 = 0

Factor a trinomial.
(-8 + x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

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

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

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {8, 6}