5p^2=-8p-3

Solution for 5p^2=-8p-3 equation:

Simplifying
5p2 = -8p + -3

Reorder the terms:
5p2 = -3 + -8p

Solving
5p2 = -3 + -8p

Solving for variable 'p'.

Reorder the terms:
3 + 8p + 5p2 = -3 + -8p + 3 + 8p

Reorder the terms:
3 + 8p + 5p2 = -3 + 3 + -8p + 8p

Combine like terms: -3 + 3 = 0
3 + 8p + 5p2 = 0 + -8p + 8p
3 + 8p + 5p2 = -8p + 8p

Combine like terms: -8p + 8p = 0
3 + 8p + 5p2 = 0

Factor a trinomial.
(1 + p)(3 + 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 '(3 + 5p)' equal to zero and attempt to solve:

Simplifying
3 + 5p = 0

Solving
3 + 5p = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5p = 0 + -3
5p = 0 + -3

Combine like terms: 0 + -3 = -3
5p = -3

Divide each side by '5'.
p = -0.6

Simplifying
p = -0.6
Solution
p = {-1, -0.6}