6p^4=p^2+2

Solution for 6p^4=p^2+2 equation:

Simplifying
6p4 = p2 + 2

Reorder the terms:
6p4 = 2 + p2

Solving
6p4 = 2 + p2

Solving for variable 'p'.

Reorder the terms:
-2 + -1p2 + 6p4 = 2 + p2 + -2 + -1p2

Reorder the terms:
-2 + -1p2 + 6p4 = 2 + -2 + p2 + -1p2

Combine like terms: 2 + -2 = 0
-2 + -1p2 + 6p4 = 0 + p2 + -1p2
-2 + -1p2 + 6p4 = p2 + -1p2

Combine like terms: p2 + -1p2 = 0
-2 + -1p2 + 6p4 = 0

Factor a trinomial.
(-1 + -2p2)(2 + -3p2) = 0

Subproblem 1
Set the factor '(-1 + -2p2)' equal to zero and attempt to solve:

Simplifying
-1 + -2p2 = 0

Solving
-1 + -2p2 = 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 + -2p2 = 0 + 1

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

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

Divide each side by '-2'.
p2 = -0.5

Simplifying
p2 = -0.5

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 '(2 + -3p2)' equal to zero and attempt to solve:

Simplifying
2 + -3p2 = 0

Solving
2 + -3p2 = 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 + -3p2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3p2 = 0 + -2
-3p2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3p2 = -2

Divide each side by '-3'.
p2 = 0.6666666667

Simplifying
p2 = 0.6666666667

Take the square root of each side:
p = {-0.816496581, 0.816496581}
Solution
p = {-0.816496581, 0.816496581}