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.
(-1 + -1p2)(6 + -1p2) = 0

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

Simplifying
-1 + -1p2 = 0

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

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

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

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

Simplifying
p2 = -1

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 '(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

Take the square root of each side:
p = {-2.449489743, 2.449489743}
Solution
p = {-2.449489743, 2.449489743}