-4p^2-4p-1=0

Solution for -4p^2-4p-1=0 equation:

Simplifying
-4p2 + -4p + -1 = 0

Reorder the terms:
-1 + -4p + -4p2 = 0

Solving
-1 + -4p + -4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 4p + 4p2) = 0

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

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

Simplifying
1 + 2p = 0

Solving
1 + 2p = 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 + 2p = 0 + -1

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

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

Divide each side by '2'.
p = -0.5

Simplifying
p = -0.5
Subproblem 2
Set the factor '(1 + 2p)' equal to zero and attempt to solve:

Simplifying
1 + 2p = 0

Solving
1 + 2p = 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 + 2p = 0 + -1

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

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

Divide each side by '2'.
p = -0.5

Simplifying
p = -0.5
Solution
p = {-0.5, -0.5}