p^2=54-3p

Solution for p^2=54-3p equation:

Simplifying
p2 = 54 + -3p

Solving
p2 = 54 + -3p

Solving for variable 'p'.

Reorder the terms:
-54 + 3p + p2 = 54 + -3p + -54 + 3p

Reorder the terms:
-54 + 3p + p2 = 54 + -54 + -3p + 3p

Combine like terms: 54 + -54 = 0
-54 + 3p + p2 = 0 + -3p + 3p
-54 + 3p + p2 = -3p + 3p

Combine like terms: -3p + 3p = 0
-54 + 3p + p2 = 0

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

Subproblem 1
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
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}