54-15p=p^2

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

Simplifying
54 + -15p = p2

Solving
54 + -15p = p2

Solving for variable 'p'.

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

Factor a trinomial.
(3 + -1p)(18 + p) = 0

Subproblem 1
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Subproblem 2
Set the factor '(18 + p)' equal to zero and attempt to solve:

Simplifying
18 + p = 0

Solving
18 + p = 0

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

Add '-18' to each side of the equation.
18 + -18 + p = 0 + -18

Combine like terms: 18 + -18 = 0
0 + p = 0 + -18
p = 0 + -18

Combine like terms: 0 + -18 = -18
p = -18

Simplifying
p = -18
Solution
p = {3, -18}