4p^2+22p+10=0

Solution for 4p^2+22p+10=0 equation:

Simplifying
4p2 + 22p + 10 = 0

Reorder the terms:
10 + 22p + 4p2 = 0

Solving
10 + 22p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 11p + 2p2) = 0

Factor a trinomial.
2((5 + p)(1 + 2p)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + p)' equal to zero and attempt to solve:

Simplifying
5 + p = 0

Solving
5 + p = 0

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

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

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

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

Simplifying
p = -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 = {-5, -0.5}