4p^2+24p+32=0

Solution for 4p^2+24p+32=0 equation:

Simplifying
4p2 + 24p + 32 = 0

Reorder the terms:
32 + 24p + 4p2 = 0

Solving
32 + 24p + 4p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + 6p + p2) = 0

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

Ignore the factor 4.
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 + p)' equal to zero and attempt to solve:

Simplifying
2 + p = 0

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

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

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

Simplifying
p = -2
Solution
p = {-4, -2}