9p^4-p^2=0

Solution for 9p^4-p^2=0 equation:

Simplifying
9p4 + -1p2 = 0

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

Solving
-1p2 + 9p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p2'.
p2(-1 + 9p2) = 0

Factor a difference between two squares.
p2((1 + 3p)(-1 + 3p)) = 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 + 3p)' equal to zero and attempt to solve:

Simplifying
1 + 3p = 0

Solving
1 + 3p = 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 + 3p = 0 + -1

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

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

Divide each side by '3'.
p = -0.3333333333

Simplifying
p = -0.3333333333
Subproblem 3
Set the factor '(-1 + 3p)' equal to zero and attempt to solve:

Simplifying
-1 + 3p = 0

Solving
-1 + 3p = 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 + 3p = 0 + 1

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

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

Divide each side by '3'.
p = 0.3333333333

Simplifying
p = 0.3333333333
Solution
p = {0, -0.3333333333, 0.3333333333}