p(5p+6)(5p-6)=

Solution for p(5p+6)(5p-6)= equation:

Simplifying
p(5p + 6)(5p + -6) = 0

Reorder the terms:
p(6 + 5p)(5p + -6) = 0

Reorder the terms:
p(6 + 5p)(-6 + 5p) = 0

Multiply (6 + 5p) * (-6 + 5p)
p(6(-6 + 5p) + 5p * (-6 + 5p)) = 0
p((-6 * 6 + 5p * 6) + 5p * (-6 + 5p)) = 0
p((-36 + 30p) + 5p * (-6 + 5p)) = 0
p(-36 + 30p + (-6 * 5p + 5p * 5p)) = 0
p(-36 + 30p + (-30p + 25p2)) = 0

Combine like terms: 30p + -30p = 0
p(-36 + 0 + 25p2) = 0
p(-36 + 25p2) = 0
(-36 * p + 25p2 * p) = 0
(-36p + 25p3) = 0

Solving
-36p + 25p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(-36 + 25p2) = 0

Factor a difference between two squares.
p((6 + 5p)(-6 + 5p)) = 0

Subproblem 1
Set the factor 'p' equal to zero and attempt to solve:

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0
Subproblem 2
Set the factor '(6 + 5p)' equal to zero and attempt to solve:

Simplifying
6 + 5p = 0

Solving
6 + 5p = 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 + 5p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5p = 0 + -6
5p = 0 + -6

Combine like terms: 0 + -6 = -6
5p = -6

Divide each side by '5'.
p = -1.2

Simplifying
p = -1.2
Subproblem 3
Set the factor '(-6 + 5p)' equal to zero and attempt to solve:

Simplifying
-6 + 5p = 0

Solving
-6 + 5p = 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 + 5p = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 5p = 0 + 6
5p = 0 + 6

Combine like terms: 0 + 6 = 6
5p = 6

Divide each side by '5'.
p = 1.2

Simplifying
p = 1.2
Solution
p = {0, -1.2, 1.2}