4X^2-X^4=3

Solution for 4X^2-X^4=3 equation:

Simplifying
4X2 + -1X4 = 3

Solving
4X2 + -1X4 = 3

Solving for variable 'X'.

Reorder the terms:
-3 + 4X2 + -1X4 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 4X2 + -1X4 = 0

Factor a trinomial.
(-3 + X2)(1 + -1X2) = 0

Factor a difference between two squares.
(-3 + X2)((1 + X)(1 + -1X)) = 0

Subproblem 1
Set the factor '(-3 + X2)' equal to zero and attempt to solve:

Simplifying
-3 + X2 = 0

Solving
-3 + X2 = 0

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

Add '3' to each side of the equation.
-3 + 3 + X2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + X2 = 0 + 3
X2 = 0 + 3

Combine like terms: 0 + 3 = 3
X2 = 3

Simplifying
X2 = 3

Take the square root of each side:
X = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(1 + X)' equal to zero and attempt to solve:

Simplifying
1 + X = 0

Solving
1 + X = 0

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

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

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

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

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

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

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

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

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

Simplifying
X = 1
Solution
X = {-1.732050808, 1.732050808, -1, 1}