5p^2+20p+5=-10

Solution for 5p^2+20p+5=-10 equation:

Simplifying
5p2 + 20p + 5 = -10

Reorder the terms:
5 + 20p + 5p2 = -10

Solving
5 + 20p + 5p2 = -10

Solving for variable 'p'.

Reorder the terms:
5 + 10 + 20p + 5p2 = -10 + 10

Combine like terms: 5 + 10 = 15
15 + 20p + 5p2 = -10 + 10

Combine like terms: -10 + 10 = 0
15 + 20p + 5p2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + 4p + p2) = 0

Factor a trinomial.
5((3 + p)(1 + p)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 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 + p = 0 + -3

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

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

Simplifying
p = -3
Subproblem 2
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
Solution
p = {-3, -1}