p^2(64-p^2)-9(64-p^2)=0

Solution for p^2(64-p^2)-9(64-p^2)=0 equation:

Simplifying
p2(64 + -1p2) + -9(64 + -1p2) = 0
(64 * p2 + -1p2 * p2) + -9(64 + -1p2) = 0
(64p2 + -1p4) + -9(64 + -1p2) = 0
64p2 + -1p4 + (64 * -9 + -1p2 * -9) = 0
64p2 + -1p4 + (-576 + 9p2) = 0

Reorder the terms:
-576 + 64p2 + 9p2 + -1p4 = 0

Combine like terms: 64p2 + 9p2 = 73p2
-576 + 73p2 + -1p4 = 0

Solving
-576 + 73p2 + -1p4 = 0

Solving for variable 'p'.

Factor a trinomial.
(-64 + p2)(9 + -1p2) = 0

Factor a difference between two squares.
((8 + p)(-8 + p))(9 + -1p2) = 0

Factor a difference between two squares.
((3 + p)(3 + -1p))(8 + p)(-8 + p) = 0

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

Simplifying
8 + p = 0

Solving
8 + p = 0

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

Add '-8' to each side of the equation.
8 + -8 + p = 0 + -8

Combine like terms: 8 + -8 = 0
0 + p = 0 + -8
p = 0 + -8

Combine like terms: 0 + -8 = -8
p = -8

Simplifying
p = -8
Subproblem 2
Set the factor '(-8 + p)' equal to zero and attempt to solve:

Simplifying
-8 + p = 0

Solving
-8 + p = 0

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

Add '8' to each side of the equation.
-8 + 8 + p = 0 + 8

Combine like terms: -8 + 8 = 0
0 + p = 0 + 8
p = 0 + 8

Combine like terms: 0 + 8 = 8
p = 8

Simplifying
p = 8
Subproblem 3
Set the factor '(3 + p)' equal to zero and attempt to solve:

Simplifying
3 + p = 0

Solving
3 + p = 0

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

Add '-3' to each side of the equation.
3 + -3 + p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3

Combine like terms: 0 + -3 = -3
p = -3

Simplifying
p = -3
Subproblem 4
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3
Solution
p = {-8, 8, -3, 3}