p^4+5p^2-6=0

Solution for p^4+5p^2-6=0 equation:

Simplifying
p4 + 5p2 + -6 = 0

Reorder the terms:
-6 + 5p2 + p4 = 0

Solving
-6 + 5p2 + p4 = 0

Solving for variable 'p'.

Factor a trinomial.
(-6 + -1p2)(1 + -1p2) = 0

Factor a difference between two squares.
(-6 + -1p2)((1 + p)(1 + -1p)) = 0

Subproblem 1
Set the factor '(-6 + -1p2)' equal to zero and attempt to solve:

Simplifying
-6 + -1p2 = 0

Solving
-6 + -1p2 = 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 + -1p2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1p2 = 0 + 6
-1p2 = 0 + 6

Combine like terms: 0 + 6 = 6
-1p2 = 6

Divide each side by '-1'.
p2 = -6

Simplifying
p2 = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + p)' equal to zero and attempt to solve:

Simplifying
1 + p = 0

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

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

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

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

Simplifying
1 + -1p = 0

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

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

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

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

Simplifying
p = 1
Solution
p = {-1, 1}