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

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

Simplifying
p4 + -4p2 + 3 = 0

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

Solving
3 + -4p2 + p4 = 0

Solving for variable 'p'.

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

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

Take the square root of each side:
p = {-1.732050808, 1.732050808}
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 = {-1.732050808, 1.732050808, -1, 1}