15p-54=p^2

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

Simplifying
15p + -54 = p2

Reorder the terms:
-54 + 15p = p2

Solving
-54 + 15p = p2

Solving for variable 'p'.

Combine like terms: p2 + -1p2 = 0
-54 + 15p + -1p2 = 0

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

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

Simplifying
-9 + p = 0

Solving
-9 + p = 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 + p = 0 + 9

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

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

Simplifying
p = 9
Subproblem 2
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
Solution
p = {9, 6}