Q^2-12Q=-32

Solution for Q^2-12Q=-32 equation:

Simplifying
Q2 + -12Q = -32

Reorder the terms:
-12Q + Q2 = -32

Solving
-12Q + Q2 = -32

Solving for variable 'Q'.

Reorder the terms:
32 + -12Q + Q2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -12Q + Q2 = 0

Factor a trinomial.
(4 + -1Q)(8 + -1Q) = 0

Subproblem 1
Set the factor '(4 + -1Q)' equal to zero and attempt to solve:

Simplifying
4 + -1Q = 0

Solving
4 + -1Q = 0

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

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

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

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

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

Simplifying
Q = 4
Subproblem 2
Set the factor '(8 + -1Q)' equal to zero and attempt to solve:

Simplifying
8 + -1Q = 0

Solving
8 + -1Q = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1Q = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1Q = 0 + -8
-1Q = 0 + -8

Combine like terms: 0 + -8 = -8
-1Q = -8

Divide each side by '-1'.
Q = 8

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