4p^4+11p^2-3=0

Solution for 4p^4+11p^2-3=0 equation:

Simplifying
4p4 + 11p2 + -3 = 0

Reorder the terms:
-3 + 11p2 + 4p4 = 0

Solving
-3 + 11p2 + 4p4 = 0

Solving for variable 'p'.

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

Factor a difference between two squares.
(-3 + -1p2)((1 + 2p)(1 + -2p)) = 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 '(1 + 2p)' equal to zero and attempt to solve:

Simplifying
1 + 2p = 0

Solving
1 + 2p = 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 + 2p = 0 + -1

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

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

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

Simplifying
p = -0.5
Subproblem 3
Set the factor '(1 + -2p)' equal to zero and attempt to solve:

Simplifying
1 + -2p = 0

Solving
1 + -2p = 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 + -2p = 0 + -1

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

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

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

Simplifying
p = 0.5
Solution
p = {-0.5, 0.5}