12x-5=2x^2+13

Solution for 12x-5=2x^2+13 equation:

Simplifying
12x + -5 = 2x2 + 13

Reorder the terms:
-5 + 12x = 2x2 + 13

Reorder the terms:
-5 + 12x = 13 + 2x2

Solving
-5 + 12x = 13 + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + -13 + 12x + -2x2 = 13 + 2x2 + -13 + -2x2

Combine like terms: -5 + -13 = -18
-18 + 12x + -2x2 = 13 + 2x2 + -13 + -2x2

Reorder the terms:
-18 + 12x + -2x2 = 13 + -13 + 2x2 + -2x2

Combine like terms: 13 + -13 = 0
-18 + 12x + -2x2 = 0 + 2x2 + -2x2
-18 + 12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-18 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 6x + -1x2) = 0

Factor a trinomial.
2((-3 + x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 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 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Subproblem 2
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
Solution
x = {3, 3}