p(p-22)=-120

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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}

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