p^4-p^2=12

Solution for p^4-p^2=12 equation:

Simplifying
p4 + -1p2 = 12

Reorder the terms:
-1p2 + p4 = 12

Solving
-1p2 + p4 = 12

Solving for variable 'p'.

Reorder the terms:
-12 + -1p2 + p4 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + -1p2 + p4 = 0

Factor a trinomial.
(-3 + -1p2)(4 + -1p2) = 0

Factor a difference between two squares.
(-3 + -1p2)((2 + p)(2 + -1p)) = 0

Subproblem 1
Set the factor '(-3 + -1p2)' equal to zero and attempt to solve:

Simplifying
-3 + -1p2 = 0

Solving
-3 + -1p2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1p2 = 0 + 3
-1p2 = 0 + 3

Combine like terms: 0 + 3 = 3
-1p2 = 3

Divide each side by '-1'.
p2 = -3

Simplifying
p2 = -3

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 + 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 3
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 = {-2, 2}