4p^2-12p=72

Solution for 4p^2-12p=72 equation:

Simplifying
4p2 + -12p = 72

Reorder the terms:
-12p + 4p2 = 72

Solving
-12p + 4p2 = 72

Solving for variable 'p'.

Reorder the terms:
-72 + -12p + 4p2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -12p + 4p2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-18 + -3p + p2) = 0

Factor a trinomial.
4((-3 + -1p)(6 + -1p)) = 0

Ignore the factor 4.
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 '(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 = {-3, 6}