6x^4+-17x^2+12=0

Solution for 6x^4+-17x^2+12=0 equation:

Simplifying
6x4 + -17x2 + 12 = 0

Reorder the terms:
12 + -17x2 + 6x4 = 0

Solving
12 + -17x2 + 6x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -3x2)(3 + -2x2) = 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 '(3 + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x2 = 0

Solving
3 + -2x2 = 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 + -2x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x2 = 0 + -3
-2x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x2 = -3

Divide each side by '-2'.
x2 = 1.5

Simplifying
x2 = 1.5

Take the square root of each side:
x = {-1.224744871, 1.224744871}
Solution
x = {-1.154700538, 1.154700538, -1.224744871, 1.224744871}