4x^4-19x^2+12=0

Solution for 4x^4-19x^2+12=0 equation:

Simplifying
4x4 + -19x2 + 12 = 0

Reorder the terms:
12 + -19x2 + 4x4 = 0

Solving
12 + -19x2 + 4x4 = 0

Solving for variable 'x'.

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

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

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

Simplifying
3 + -4x2 = 0

Solving
3 + -4x2 = 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 + -4x2 = 0 + -3

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

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

Divide each side by '-4'.
x2 = 0.75

Simplifying
x2 = 0.75

Take the square root of each side:
x = {-0.866025404, 0.866025404}
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-0.866025404, 0.866025404, -2, 2}