p(p-20)=-96

Solution for p(p-20)=-96 equation:

Simplifying
p(p + -20) = -96

Reorder the terms:
p(-20 + p) = -96
(-20 * p + p * p) = -96
(-20p + p2) = -96

Solving
-20p + p2 = -96

Solving for variable 'p'.

Reorder the terms:
96 + -20p + p2 = -96 + 96

Combine like terms: -96 + 96 = 0
96 + -20p + p2 = 0

Factor a trinomial.
(8 + -1p)(12 + -1p) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(12 + -1p)' equal to zero and attempt to solve:

Simplifying
12 + -1p = 0

Solving
12 + -1p = 0

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

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

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

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

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

Simplifying
p = 12
Solution
p = {8, 12}