p(p-22)=-120

Solution for p(p-22)=-120 equation:

Simplifying
p(p + -22) = -120

Reorder the terms:
p(-22 + p) = -120
(-22 * p + p * p) = -120
(-22p + p2) = -120

Solving
-22p + p2 = -120

Solving for variable 'p'.

Reorder the terms:
120 + -22p + p2 = -120 + 120

Combine like terms: -120 + 120 = 0
120 + -22p + p2 = 0

Factor a trinomial.
(10 + -1p)(12 + -1p) = 0

Subproblem 1
Set the factor '(10 + -1p)' equal to zero and attempt to solve:

Simplifying
10 + -1p = 0

Solving
10 + -1p = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1p = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1p = 0 + -10
-1p = 0 + -10

Combine like terms: 0 + -10 = -10
-1p = -10

Divide each side by '-1'.
p = 10

Simplifying
p = 10
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 = {10, 12}