x^2-12x+32=3x-4

Solution for x^2-12x+32=3x-4 equation:

Simplifying
x2 + -12x + 32 = 3x + -4

Reorder the terms:
32 + -12x + x2 = 3x + -4

Reorder the terms:
32 + -12x + x2 = -4 + 3x

Solving
32 + -12x + x2 = -4 + 3x

Solving for variable 'x'.

Reorder the terms:
32 + 4 + -12x + -3x + x2 = -4 + 3x + 4 + -3x

Combine like terms: 32 + 4 = 36
36 + -12x + -3x + x2 = -4 + 3x + 4 + -3x

Combine like terms: -12x + -3x = -15x
36 + -15x + x2 = -4 + 3x + 4 + -3x

Reorder the terms:
36 + -15x + x2 = -4 + 4 + 3x + -3x

Combine like terms: -4 + 4 = 0
36 + -15x + x2 = 0 + 3x + -3x
36 + -15x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
36 + -15x + x2 = 0

Factor a trinomial.
(3 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {3, 12}