3p^2+9p-122=-2

Solution for 3p^2+9p-122=-2 equation:

Simplifying
3p2 + 9p + -122 = -2

Reorder the terms:
-122 + 9p + 3p2 = -2

Solving
-122 + 9p + 3p2 = -2

Solving for variable 'p'.

Reorder the terms:
-122 + 2 + 9p + 3p2 = -2 + 2

Combine like terms: -122 + 2 = -120
-120 + 9p + 3p2 = -2 + 2

Combine like terms: -2 + 2 = 0
-120 + 9p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-40 + 3p + p2) = 0

Factor a trinomial.
3((-8 + -1p)(5 + -1p)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-8 + -1p)' equal to zero and attempt to solve:

Simplifying
-8 + -1p = 0

Solving
-8 + -1p = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1p = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1p = 0 + 8
-1p = 0 + 8

Combine like terms: 0 + 8 = 8
-1p = 8

Divide each side by '-1'.
p = -8

Simplifying
p = -8
Subproblem 2
Set the factor '(5 + -1p)' equal to zero and attempt to solve:

Simplifying
5 + -1p = 0

Solving
5 + -1p = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1p = 0 + -5
-1p = 0 + -5

Combine like terms: 0 + -5 = -5
-1p = -5

Divide each side by '-1'.
p = 5

Simplifying
p = 5
Solution
p = {-8, 5}