12x^4=19x^2-4

Solution for 12x^4=19x^2-4 equation:

Simplifying
12x4 = 19x2 + -4

Reorder the terms:
12x4 = -4 + 19x2

Solving
12x4 = -4 + 19x2

Solving for variable 'x'.

Reorder the terms:
4 + -19x2 + 12x4 = -4 + 19x2 + 4 + -19x2

Reorder the terms:
4 + -19x2 + 12x4 = -4 + 4 + 19x2 + -19x2

Combine like terms: -4 + 4 = 0
4 + -19x2 + 12x4 = 0 + 19x2 + -19x2
4 + -19x2 + 12x4 = 19x2 + -19x2

Combine like terms: 19x2 + -19x2 = 0
4 + -19x2 + 12x4 = 0

Factor a trinomial.
(1 + -4x2)(4 + -3x2) = 0

Factor a difference between two squares.
((1 + 2x)(1 + -2x))(4 + -3x2) = 0

Subproblem 1
Set the factor '(4 + -3x2)' equal to zero and attempt to solve:

Simplifying
4 + -3x2 = 0

Solving
4 + -3x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x2 = 0 + -4
-3x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-3x2 = -4

Divide each side by '-3'.
x2 = 1.333333333

Simplifying
x2 = 1.333333333

Take the square root of each side:
x = {-1.154700538, 1.154700538}
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

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

Simplifying
x = 0.5
Solution
x = {-1.154700538, 1.154700538, -0.5, 0.5}