-7p^2-31p-12=0

Solution for -7p^2-31p-12=0 equation:

Simplifying
-7p2 + -31p + -12 = 0

Reorder the terms:
-12 + -31p + -7p2 = 0

Solving
-12 + -31p + -7p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 31p + 7p2) = 0

Factor a trinomial.
-1((4 + p)(3 + 7p)) = 0

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

Simplifying
4 + p = 0

Solving
4 + p = 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 + p = 0 + -4

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

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

Simplifying
p = -4
Subproblem 2
Set the factor '(3 + 7p)' equal to zero and attempt to solve:

Simplifying
3 + 7p = 0

Solving
3 + 7p = 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 + 7p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7p = 0 + -3
7p = 0 + -3

Combine like terms: 0 + -3 = -3
7p = -3

Divide each side by '7'.
p = -0.4285714286

Simplifying
p = -0.4285714286
Solution
p = {-4, -0.4285714286}