12p^2-31p-15=0

Solution for 12p^2-31p-15=0 equation:

Simplifying
12p2 + -31p + -15 = 0

Reorder the terms:
-15 + -31p + 12p2 = 0

Solving
-15 + -31p + 12p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-5 + -12p)(3 + -1p) = 0

Subproblem 1
Set the factor '(-5 + -12p)' equal to zero and attempt to solve:

Simplifying
-5 + -12p = 0

Solving
-5 + -12p = 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 + -12p = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -12p = 0 + 5
-12p = 0 + 5

Combine like terms: 0 + 5 = 5
-12p = 5

Divide each side by '-12'.
p = -0.4166666667

Simplifying
p = -0.4166666667
Subproblem 2
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
Solution
p = {-0.4166666667, 3}