16p^2-48p-64=0

Solution for 16p^2-48p-64=0 equation:

Simplifying
16p2 + -48p + -64 = 0

Reorder the terms:
-64 + -48p + 16p2 = 0

Solving
-64 + -48p + 16p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-4 + -3p + p2) = 0

Factor a trinomial.
16((-1 + -1p)(4 + -1p)) = 0

Ignore the factor 16.
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}