0=(4x^4)-(12x^2)-3

Solution for 0=(4x^4)-(12x^2)-3 equation:

Simplifying
0 = (4x4) + -1(12x2) + -3

Remove parenthesis around (12x2)
0 = (4x4) + -1 * 12x2 + -3

Multiply -1 * 12
0 = (4x4) + -12x2 + -3

Reorder the terms:
0 = -3 + -12x2 + (4x4)

Solving
0 = -3 + -12x2 + (4x4)

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + 12x2 + (-4x4) = -3 + -12x2 + (4x4) + 3 + 12x2 + (-4x4)

Reorder the terms:
3 + 12x2 + (-4x4) = -3 + 3 + -12x2 + 12x2 + (4x4) + (-4x4)

Combine like terms: -3 + 3 = 0
3 + 12x2 + (-4x4) = 0 + -12x2 + 12x2 + (4x4) + (-4x4)
3 + 12x2 + (-4x4) = -12x2 + 12x2 + (4x4) + (-4x4)

Combine like terms: -12x2 + 12x2 = 0
3 + 12x2 + (-4x4) = 0 + (4x4) + (-4x4)
3 + 12x2 + (-4x4) = (4x4) + (-4x4)

Combine like terms: (4x4) + (-4x4) = 0
3 + 12x2 + (-4x4) = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.75 + -3x2 + x4 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -3x2 + 0.75 + x4 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -3x2 + x4 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -3x2 + x4 = 0 + 0.75
-3x2 + x4 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-3x2 + x4 = 0.75

The x term is -3x2.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x2 + 2.25 + x4 = 0.75 + 2.25

Reorder the terms:
2.25 + -3x2 + x4 = 0.75 + 2.25

Combine like terms: 0.75 + 2.25 = 3
2.25 + -3x2 + x4 = 3

Factor a perfect square on the left side:
((x2) + -1.5)((x2) + -1.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
((x2) + -1.5) equal to 1.732050808 and -1.732050808.

Subproblem 1
(x2) + -1.5 = 1.732050808

Simplifying
(x2) + -1.5 = 1.732050808
x2 + -1.5 = 1.732050808

Reorder the terms:
-1.5 + x2 = 1.732050808

Solving
-1.5 + x2 = 1.732050808

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x2 = 1.732050808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x2 = 1.732050808 + 1.5
x2 = 1.732050808 + 1.5

Combine like terms: 1.732050808 + 1.5 = 3.232050808
x2 = 3.232050808

Simplifying
x2 = 3.232050808

Take the square root of each side:
x = {-1.797790535, 1.797790535}

Subproblem 2
(x2) + -1.5 = -1.732050808

Simplifying
(x2) + -1.5 = -1.732050808
x2 + -1.5 = -1.732050808

Reorder the terms:
-1.5 + x2 = -1.732050808

Solving
-1.5 + x2 = -1.732050808

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x2 = -1.732050808 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x2 = -1.732050808 + 1.5
x2 = -1.732050808 + 1.5

Combine like terms: -1.732050808 + 1.5 = -0.232050808
x2 = -0.232050808

Simplifying
x2 = -0.232050808

Reorder the terms:
0.232050808 + x2 = -0.232050808 + 0.232050808

Combine like terms: -0.232050808 + 0.232050808 = 0.000000000
0.232050808 + x2 = 0.000000000

The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.