p^2=-6p+72

Solution for p^2=-6p+72 equation:

Simplifying
p2 = -6p + 72

Reorder the terms:
p2 = 72 + -6p

Solving
p2 = 72 + -6p

Solving for variable 'p'.

Reorder the terms:
-72 + 6p + p2 = 72 + -6p + -72 + 6p

Reorder the terms:
-72 + 6p + p2 = 72 + -72 + -6p + 6p

Combine like terms: 72 + -72 = 0
-72 + 6p + p2 = 0 + -6p + 6p
-72 + 6p + p2 = -6p + 6p

Combine like terms: -6p + 6p = 0
-72 + 6p + p2 = 0

Factor a trinomial.
(-12 + -1p)(6 + -1p) = 0

Subproblem 1
Set the factor '(-12 + -1p)' equal to zero and attempt to solve:

Simplifying
-12 + -1p = 0

Solving
-12 + -1p = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1p = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1p = 0 + 12
-1p = 0 + 12

Combine like terms: 0 + 12 = 12
-1p = 12

Divide each side by '-1'.
p = -12

Simplifying
p = -12
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 = {-12, 6}