p(p-1)=20

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Solution for p(p-1)=20 equation:


Simplifying
p(p + -1) = 20

Reorder the terms:
p(-1 + p) = 20
(-1 * p + p * p) = 20
(-1p + p2) = 20

Solving
-1p + p2 = 20

Solving for variable 'p'.

Reorder the terms:
-20 + -1p + p2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -1p + p2 = 0

Factor a trinomial.
(-4 + -1p)(5 + -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 '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5

Solution

p = {-4, 5}

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