3x^4-27x^2+42=0

Solution for 3x^4-27x^2+42=0 equation:

Simplifying
3x4 + -27x2 + 42 = 0

Reorder the terms:
42 + -27x2 + 3x4 = 0

Solving
42 + -27x2 + 3x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -9x2 + x4) = 0

Factor a trinomial.
3((2 + -1x2)(7 + -1x2)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve:

Simplifying
2 + -1x2 = 0

Solving
2 + -1x2 = 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 + -1x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x2 = 0 + -2
-1x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1x2 = -2

Divide each side by '-1'.
x2 = 2

Simplifying
x2 = 2

Take the square root of each side:
x = {-1.414213562, 1.414213562}
Subproblem 2
Set the factor '(7 + -1x2)' equal to zero and attempt to solve:

Simplifying
7 + -1x2 = 0

Solving
7 + -1x2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x2 = 0 + -7
-1x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1x2 = -7

Divide each side by '-1'.
x2 = 7

Simplifying
x2 = 7

Take the square root of each side:
x = {-2.645751311, 2.645751311}
Solution
x = {-1.414213562, 1.414213562, -2.645751311, 2.645751311}