5p^2=-6p-1

Solution for 5p^2=-6p-1 equation:

Simplifying
5p2 = -6p + -1

Reorder the terms:
5p2 = -1 + -6p

Solving
5p2 = -1 + -6p

Solving for variable 'p'.

Reorder the terms:
1 + 6p + 5p2 = -1 + -6p + 1 + 6p

Reorder the terms:
1 + 6p + 5p2 = -1 + 1 + -6p + 6p

Combine like terms: -1 + 1 = 0
1 + 6p + 5p2 = 0 + -6p + 6p
1 + 6p + 5p2 = -6p + 6p

Combine like terms: -6p + 6p = 0
1 + 6p + 5p2 = 0

Factor a trinomial.
(1 + p)(1 + 5p) = 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 + 5p)' equal to zero and attempt to solve:

Simplifying
1 + 5p = 0

Solving
1 + 5p = 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 + 5p = 0 + -1

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

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

Divide each side by '5'.
p = -0.2

Simplifying
p = -0.2
Solution
p = {-1, -0.2}