12x-32=x(x)

Solution for 12x-32=x(x) equation:

Simplifying
12x + -32 = x(x)

Reorder the terms:
-32 + 12x = x(x)

Multiply x * x
-32 + 12x = x2

Solving
-32 + 12x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
-32 + 12x + -1x2 = 0

Factor a trinomial.
(-8 + x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {8, 4}