2p^2-24p=-72

Solution for 2p^2-24p=-72 equation:

Simplifying
2p2 + -24p = -72

Reorder the terms:
-24p + 2p2 = -72

Solving
-24p + 2p2 = -72

Solving for variable 'p'.

Reorder the terms:
72 + -24p + 2p2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + -24p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + -12p + p2) = 0

Factor a trinomial.
2((6 + -1p)(6 + -1p)) = 0

Ignore the factor 2.
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 '(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 = {6, 6}