p^5-6p^3+8p=0

Solution for p^5-6p^3+8p=0 equation:

Simplifying
p5 + -6p3 + 8p = 0

Reorder the terms:
8p + -6p3 + p5 = 0

Solving
8p + -6p3 + p5 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(8 + -6p2 + p4) = 0

Factor a trinomial.
p((2 + -1p2)(4 + -1p2)) = 0

Factor a difference between two squares.
p((2 + -1p2)((2 + p)(2 + -1p))) = 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 '(2 + -1p2)' equal to zero and attempt to solve:

Simplifying
2 + -1p2 = 0

Solving
2 + -1p2 = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p2 = 0 + -2
-1p2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1p2 = -2

Divide each side by '-1'.
p2 = 2

Simplifying
p2 = 2

Take the square root of each side:
p = {-1.414213562, 1.414213562}
Subproblem 3
Set the factor '(2 + p)' equal to zero and attempt to solve:

Simplifying
2 + p = 0

Solving
2 + p = 0

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

Add '-2' to each side of the equation.
2 + -2 + p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + p = 0 + -2
p = 0 + -2

Combine like terms: 0 + -2 = -2
p = -2

Simplifying
p = -2
Subproblem 4
Set the factor '(2 + -1p)' equal to zero and attempt to solve:

Simplifying
2 + -1p = 0

Solving
2 + -1p = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1p = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1p = 0 + -2
-1p = 0 + -2

Combine like terms: 0 + -2 = -2
-1p = -2

Divide each side by '-1'.
p = 2

Simplifying
p = 2
Solution
p = {0, -1.414213562, 1.414213562, -2, 2}