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

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

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

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

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

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

Combine like terms: -2x2 + -18x2 = -20x2
(6 + -20x2 + 6x4) = 0

Solving
6 + -20x2 + 6x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -10x2 + 3x4) = 0

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

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

Simplifying
1 + -3x2 = 0

Solving
1 + -3x2 = 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 + -3x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x2 = 0 + -1
-3x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-3x2 = -1

Divide each side by '-3'.
x2 = 0.3333333333

Simplifying
x2 = 0.3333333333

Take the square root of each side:
x = {-0.577350269, 0.577350269}
Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 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 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

Take the square root of each side:
x = {-1.732050808, 1.732050808}
Solution
x = {-0.577350269, 0.577350269, -1.732050808, 1.732050808}