3x^4-19x^2+16=0

Solution for 3x^4-19x^2+16=0 equation:

Simplifying
3x4 + -19x2 + 16 = 0

Reorder the terms:
16 + -19x2 + 3x4 = 0

Solving
16 + -19x2 + 3x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x2)(16 + -3x2) = 0

Factor a difference between two squares.
((1 + x)(1 + -1x))(16 + -3x2) = 0

Subproblem 1
Set the factor '(16 + -3x2)' equal to zero and attempt to solve:

Simplifying
16 + -3x2 = 0

Solving
16 + -3x2 = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3x2 = 0 + -16
-3x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-3x2 = -16

Divide each side by '-3'.
x2 = 5.333333333

Simplifying
x2 = 5.333333333

Take the square root of each side:
x = {-2.309401077, 2.309401077}
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 = {-2.309401077, 2.309401077, -1, 1}