8p^2-24p-37=-5

Solution for 8p^2-24p-37=-5 equation:

Simplifying
8p2 + -24p + -37 = -5

Reorder the terms:
-37 + -24p + 8p2 = -5

Solving
-37 + -24p + 8p2 = -5

Solving for variable 'p'.

Reorder the terms:
-37 + 5 + -24p + 8p2 = -5 + 5

Combine like terms: -37 + 5 = -32
-32 + -24p + 8p2 = -5 + 5

Combine like terms: -5 + 5 = 0
-32 + -24p + 8p2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + -3p + p2) = 0

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

Ignore the factor 8.
Subproblem 1
Set the factor '(-1 + -1p)' equal to zero and attempt to solve:

Simplifying
-1 + -1p = 0

Solving
-1 + -1p = 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 + -1p = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1p = 0 + 1
-1p = 0 + 1

Combine like terms: 0 + 1 = 1
-1p = 1

Divide each side by '-1'.
p = -1

Simplifying
p = -1
Subproblem 2
Set the factor '(4 + -1p)' equal to zero and attempt to solve:

Simplifying
4 + -1p = 0

Solving
4 + -1p = 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 + -1p = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1p = 0 + -4
-1p = 0 + -4

Combine like terms: 0 + -4 = -4
-1p = -4

Divide each side by '-1'.
p = 4

Simplifying
p = 4
Solution
p = {-1, 4}