p^2=18p-72

Solution for p^2=18p-72 equation:

Simplifying
p2 = 18p + -72

Reorder the terms:
p2 = -72 + 18p

Solving
p2 = -72 + 18p

Solving for variable 'p'.

Reorder the terms:
72 + -18p + p2 = -72 + 18p + 72 + -18p

Reorder the terms:
72 + -18p + p2 = -72 + 72 + 18p + -18p

Combine like terms: -72 + 72 = 0
72 + -18p + p2 = 0 + 18p + -18p
72 + -18p + p2 = 18p + -18p

Combine like terms: 18p + -18p = 0
72 + -18p + p2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
p = {6, 12}