p^2=p+20

Solution for p^2=p+20 equation:

Simplifying
p2 = p + 20

Reorder the terms:
p2 = 20 + p

Solving
p2 = 20 + p

Solving for variable 'p'.

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

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

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

Combine like terms: p + -1p = 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}