2x^2-12x+32=14

Solution for 2x^2-12x+32=14 equation:

Simplifying
2x2 + -12x + 32 = 14

Reorder the terms:
32 + -12x + 2x2 = 14

Solving
32 + -12x + 2x2 = 14

Solving for variable 'x'.

Reorder the terms:
32 + -14 + -12x + 2x2 = 14 + -14

Combine like terms: 32 + -14 = 18
18 + -12x + 2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
18 + -12x + 2x2 = 0

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

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

Ignore the factor 2.
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 '(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}