8p^2=-96+64p

Solution for 8p^2=-96+64p equation:

Simplifying
8p2 = -96 + 64p

Solving
8p2 = -96 + 64p

Solving for variable 'p'.

Reorder the terms:
96 + -64p + 8p2 = -96 + 64p + 96 + -64p

Reorder the terms:
96 + -64p + 8p2 = -96 + 96 + 64p + -64p

Combine like terms: -96 + 96 = 0
96 + -64p + 8p2 = 0 + 64p + -64p
96 + -64p + 8p2 = 64p + -64p

Combine like terms: 64p + -64p = 0
96 + -64p + 8p2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(12 + -8p + p2) = 0

Factor a trinomial.
8((2 + -1p)(6 + -1p)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 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 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Subproblem 2
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Solution
p = {2, 6}