5p^2+22p+8=0

Solution for 5p^2+22p+8=0 equation:

Simplifying
5p2 + 22p + 8 = 0

Reorder the terms:
8 + 22p + 5p2 = 0

Solving
8 + 22p + 5p2 = 0

Solving for variable 'p'.

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

Subproblem 1
Set the factor '(4 + p)' equal to zero and attempt to solve:

Simplifying
4 + p = 0

Solving
4 + p = 0

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

Add '-4' to each side of the equation.
4 + -4 + p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + p = 0 + -4
p = 0 + -4

Combine like terms: 0 + -4 = -4
p = -4

Simplifying
p = -4
Subproblem 2
Set the factor '(2 + 5p)' equal to zero and attempt to solve:

Simplifying
2 + 5p = 0

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

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

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

Divide each side by '5'.
p = -0.4

Simplifying
p = -0.4
Solution
p = {-4, -0.4}