p^2=12p-32

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

Simplifying
p2 = 12p + -32

Reorder the terms:
p2 = -32 + 12p

Solving
p2 = -32 + 12p

Solving for variable 'p'.

Reorder the terms:
32 + -12p + p2 = -32 + 12p + 32 + -12p

Reorder the terms:
32 + -12p + p2 = -32 + 32 + 12p + -12p

Combine like terms: -32 + 32 = 0
32 + -12p + p2 = 0 + 12p + -12p
32 + -12p + p2 = 12p + -12p

Combine like terms: 12p + -12p = 0
32 + -12p + p2 = 0

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

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

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

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

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

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

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

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

Simplifying
8 + -1p = 0

Solving
8 + -1p = 0

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

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

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

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

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

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