(6x^2-7)(9x^2-3)=0

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Solution for (6x^2-7)(9x^2-3)=0 equation:


Simplifying
(6x2 + -7)(9x2 + -3) = 0

Reorder the terms:
(-7 + 6x2)(9x2 + -3) = 0

Reorder the terms:
(-7 + 6x2)(-3 + 9x2) = 0

Multiply (-7 + 6x2) * (-3 + 9x2)
(-7(-3 + 9x2) + 6x2 * (-3 + 9x2)) = 0
((-3 * -7 + 9x2 * -7) + 6x2 * (-3 + 9x2)) = 0
((21 + -63x2) + 6x2 * (-3 + 9x2)) = 0
(21 + -63x2 + (-3 * 6x2 + 9x2 * 6x2)) = 0
(21 + -63x2 + (-18x2 + 54x4)) = 0

Combine like terms: -63x2 + -18x2 = -81x2
(21 + -81x2 + 54x4) = 0

Solving
21 + -81x2 + 54x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -27x2 + 18x4) = 0

Factor a trinomial.
3((1 + -3x2)(7 + -6x2)) = 0

Ignore the factor 3.

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 '(7 + -6x2)' equal to zero and attempt to solve:

Simplifying
7 + -6x2 = 0

Solving
7 + -6x2 = 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 + -6x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x2 = 0 + -7
-6x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-6x2 = -7

Divide each side by '-6'.
x2 = 1.166666667

Simplifying
x2 = 1.166666667

Take the square root of each side:
x = {-1.08012345, 1.08012345}
Solution
x = {-0.577350269, 0.577350269, -1.08012345, 1.08012345}

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