4p^2=-5p-1

Solution for 4p^2=-5p-1 equation:

Simplifying
4p2 = -5p + -1

Reorder the terms:
4p2 = -1 + -5p

Solving
4p2 = -1 + -5p

Solving for variable 'p'.

Reorder the terms:
1 + 5p + 4p2 = -1 + -5p + 1 + 5p

Reorder the terms:
1 + 5p + 4p2 = -1 + 1 + -5p + 5p

Combine like terms: -1 + 1 = 0
1 + 5p + 4p2 = 0 + -5p + 5p
1 + 5p + 4p2 = -5p + 5p

Combine like terms: -5p + 5p = 0
1 + 5p + 4p2 = 0

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

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

Simplifying
1 + p = 0

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

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

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

Simplifying
p = -1
Subproblem 2
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
Solution
p = {-1, -0.25}