6p^2-42p=-72

Solution for 6p^2-42p=-72 equation:

Simplifying
6p2 + -42p = -72

Reorder the terms:
-42p + 6p2 = -72

Solving
-42p + 6p2 = -72

Solving for variable 'p'.

Reorder the terms:
72 + -42p + 6p2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + -42p + 6p2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -7p + p2) = 0

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

Ignore the factor 6.
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 '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1p = 0 + -4
-1p = 0 + -4

Combine like terms: 0 + -4 = -4
-1p = -4

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {3, 4}