p^2=9p-20

Solution for p^2=9p-20 equation:

Simplifying
p2 = 9p + -20

Reorder the terms:
p2 = -20 + 9p

Solving
p2 = -20 + 9p

Solving for variable 'p'.

Reorder the terms:
20 + -9p + p2 = -20 + 9p + 20 + -9p

Reorder the terms:
20 + -9p + p2 = -20 + 20 + 9p + -9p

Combine like terms: -20 + 20 = 0
20 + -9p + p2 = 0 + 9p + -9p
20 + -9p + p2 = 9p + -9p

Combine like terms: 9p + -9p = 0
20 + -9p + 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}