8p^2=-32-40p

Solution for 8p^2=-32-40p equation:

Simplifying
8p2 = -32 + -40p

Solving
8p2 = -32 + -40p

Solving for variable 'p'.

Reorder the terms:
32 + 40p + 8p2 = -32 + -40p + 32 + 40p

Reorder the terms:
32 + 40p + 8p2 = -32 + 32 + -40p + 40p

Combine like terms: -32 + 32 = 0
32 + 40p + 8p2 = 0 + -40p + 40p
32 + 40p + 8p2 = -40p + 40p

Combine like terms: -40p + 40p = 0
32 + 40p + 8p2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(4 + 5p + p2) = 0

Factor a trinomial.
8((4 + p)(1 + p)) = 0

Ignore the factor 8.
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 '(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 = {-4, -1}