p^2=15p-54

Solution for p^2=15p-54 equation:

Simplifying
p2 = 15p + -54

Reorder the terms:
p2 = -54 + 15p

Solving
p2 = -54 + 15p

Solving for variable 'p'.

Reorder the terms:
54 + -15p + p2 = -54 + 15p + 54 + -15p

Reorder the terms:
54 + -15p + p2 = -54 + 54 + 15p + -15p

Combine like terms: -54 + 54 = 0
54 + -15p + p2 = 0 + 15p + -15p
54 + -15p + p2 = 15p + -15p

Combine like terms: 15p + -15p = 0
54 + -15p + p2 = 0

Factor a trinomial.
(6 + -1p)(9 + -1p) = 0

Subproblem 1
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Subproblem 2
Set the factor '(9 + -1p)' equal to zero and attempt to solve:

Simplifying
9 + -1p = 0

Solving
9 + -1p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1p = 0 + -9
-1p = 0 + -9

Combine like terms: 0 + -9 = -9
-1p = -9

Divide each side by '-1'.
p = 9

Simplifying
p = 9
Solution
p = {6, 9}