20p^2-31p-9=0

Solution for 20p^2-31p-9=0 equation:

Simplifying
20p2 + -31p + -9 = 0

Reorder the terms:
-9 + -31p + 20p2 = 0

Solving
-9 + -31p + 20p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(-1 + -4p)(9 + -5p) = 0

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

Simplifying
-1 + -4p = 0

Solving
-1 + -4p = 0

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

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

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

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

Divide each side by '-4'.
p = -0.25

Simplifying
p = -0.25
Subproblem 2
Set the factor '(9 + -5p)' equal to zero and attempt to solve:

Simplifying
9 + -5p = 0

Solving
9 + -5p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5p = 0 + -9
-5p = 0 + -9

Combine like terms: 0 + -9 = -9
-5p = -9

Divide each side by '-5'.
p = 1.8

Simplifying
p = 1.8
Solution
p = {-0.25, 1.8}