6p^2+24p-72=0

Solution for 6p^2+24p-72=0 equation:

Simplifying
6p2 + 24p + -72 = 0

Reorder the terms:
-72 + 24p + 6p2 = 0

Solving
-72 + 24p + 6p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + 4p + p2) = 0

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

Ignore the factor 6.
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 '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {-6, 2}