4p^2-2p-20=0

Solution for 4p^2-2p-20=0 equation:

Simplifying
4p2 + -2p + -20 = 0

Reorder the terms:
-20 + -2p + 4p2 = 0

Solving
-20 + -2p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -1p + 2p2) = 0

Factor a trinomial.
2((-2 + -1p)(5 + -2p)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -1p)' equal to zero and attempt to solve:

Simplifying
-2 + -1p = 0

Solving
-2 + -1p = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1p = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1p = 0 + 2
-1p = 0 + 2

Combine like terms: 0 + 2 = 2
-1p = 2

Divide each side by '-1'.
p = -2

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

Simplifying
5 + -2p = 0

Solving
5 + -2p = 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 + -2p = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2p = 0 + -5
-2p = 0 + -5

Combine like terms: 0 + -5 = -5
-2p = -5

Divide each side by '-2'.
p = 2.5

Simplifying
p = 2.5
Solution
p = {-2, 2.5}