(x^2-6)(2x^2-3)=0

Solution for (x^2-6)(2x^2-3)=0 equation:

Simplifying
(x2 + -6)(2x2 + -3) = 0

Reorder the terms:
(-6 + x2)(2x2 + -3) = 0

Reorder the terms:
(-6 + x2)(-3 + 2x2) = 0

Multiply (-6 + x2) * (-3 + 2x2)
(-6(-3 + 2x2) + x2(-3 + 2x2)) = 0
((-3 * -6 + 2x2 * -6) + x2(-3 + 2x2)) = 0
((18 + -12x2) + x2(-3 + 2x2)) = 0
(18 + -12x2 + (-3 * x2 + 2x2 * x2)) = 0
(18 + -12x2 + (-3x2 + 2x4)) = 0

Combine like terms: -12x2 + -3x2 = -15x2
(18 + -15x2 + 2x4) = 0

Solving
18 + -15x2 + 2x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -2x2)(6 + -1x2) = 0

Subproblem 1
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}
Subproblem 2
Set the factor '(6 + -1x2)' equal to zero and attempt to solve:

Simplifying
6 + -1x2 = 0

Solving
6 + -1x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x2 = 0 + -6
-1x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1x2 = -6

Divide each side by '-1'.
x2 = 6

Simplifying
x2 = 6

Take the square root of each side:
x = {-2.449489743, 2.449489743}
Solution
x = {-1.224744871, 1.224744871, -2.449489743, 2.449489743}