p(4p+1)(4p-1)=

Solution for p(4p+1)(4p-1)= equation:

Simplifying
p(4p + 1)(4p + -1) = 0

Reorder the terms:
p(1 + 4p)(4p + -1) = 0

Reorder the terms:
p(1 + 4p)(-1 + 4p) = 0

Multiply (1 + 4p) * (-1 + 4p)
p(1(-1 + 4p) + 4p * (-1 + 4p)) = 0
p((-1 * 1 + 4p * 1) + 4p * (-1 + 4p)) = 0
p((-1 + 4p) + 4p * (-1 + 4p)) = 0
p(-1 + 4p + (-1 * 4p + 4p * 4p)) = 0
p(-1 + 4p + (-4p + 16p2)) = 0

Combine like terms: 4p + -4p = 0
p(-1 + 0 + 16p2) = 0
p(-1 + 16p2) = 0
(-1 * p + 16p2 * p) = 0
(-1p + 16p3) = 0

Solving
-1p + 16p3 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(-1 + 16p2) = 0

Factor a difference between two squares.
p((1 + 4p)(-1 + 4p)) = 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 '(1 + 4p)' equal to zero and attempt to solve:

Simplifying
1 + 4p = 0

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

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

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

Divide each side by '4'.
p = -0.25

Simplifying
p = -0.25
Subproblem 3
Set the factor '(-1 + 4p)' equal to zero and attempt to solve:

Simplifying
-1 + 4p = 0

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

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

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

Divide each side by '4'.
p = 0.25

Simplifying
p = 0.25
Solution
p = {0, -0.25, 0.25}