0=16p^4-p^2

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Solution for 0=16p^4-p^2 equation: 


Simplifying
0 = 16p4 + -1p2

Reorder the terms:
0 = -1p2 + 16p4

Solving
0 = -1p2 + 16p4

Solving for variable 'p'.
Remove the zero:
p2 + -16p4 = -1p2 + 16p4 + p2 + -16p4

Reorder the terms:
p2 + -16p4 = -1p2 + p2 + 16p4 + -16p4

Combine like terms: -1p2 + p2 = 0
p2 + -16p4 = 0 + 16p4 + -16p4
p2 + -16p4 = 16p4 + -16p4

Combine like terms: 16p4 + -16p4 = 0
p2 + -16p4 = 0

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

Factor a difference between two squares.
p2((1 + 4p)(1 + -4p)) = 0


Subproblem 1
Set the factor 'p2' equal to zero and attempt to solve:

Simplifying
p2 = 0

Solving
p2 = 0

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

Simplifying
p2 = 0

Take the square root of each side:
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}

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