p^2=6p+27

Solution for p^2=6p+27 equation:

Simplifying
p2 = 6p + 27

Reorder the terms:
p2 = 27 + 6p

Solving
p2 = 27 + 6p

Solving for variable 'p'.

Reorder the terms:
-27 + -6p + p2 = 27 + 6p + -27 + -6p

Reorder the terms:
-27 + -6p + p2 = 27 + -27 + 6p + -6p

Combine like terms: 27 + -27 = 0
-27 + -6p + p2 = 0 + 6p + -6p
-27 + -6p + p2 = 6p + -6p

Combine like terms: 6p + -6p = 0
-27 + -6p + p2 = 0

Factor a trinomial.
(-3 + -1p)(9 + -1p) = 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 '(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 = {-3, 9}