2x^2-12x=32x-192

Solution for 2x^2-12x=32x-192 equation:

Simplifying
2x2 + -12x = 32x + -192

Reorder the terms:
-12x + 2x2 = 32x + -192

Reorder the terms:
-12x + 2x2 = -192 + 32x

Solving
-12x + 2x2 = -192 + 32x

Solving for variable 'x'.

Reorder the terms:
192 + -12x + -32x + 2x2 = -192 + 32x + 192 + -32x

Combine like terms: -12x + -32x = -44x
192 + -44x + 2x2 = -192 + 32x + 192 + -32x

Reorder the terms:
192 + -44x + 2x2 = -192 + 192 + 32x + -32x

Combine like terms: -192 + 192 = 0
192 + -44x + 2x2 = 0 + 32x + -32x
192 + -44x + 2x2 = 32x + -32x

Combine like terms: 32x + -32x = 0
192 + -44x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(96 + -22x + x2) = 0

Factor a trinomial.
2((6 + -1x)(16 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {6, 16}