(6x^2-7x+3)(2x^2-4x+6)=0

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Solution for (6x^2-7x+3)(2x^2-4x+6)=0 equation: 


Simplifying
(6x2 + -7x + 3)(2x2 + -4x + 6) = 0

Reorder the terms:
(3 + -7x + 6x2)(2x2 + -4x + 6) = 0

Reorder the terms:
(3 + -7x + 6x2)(6 + -4x + 2x2) = 0

Multiply (3 + -7x + 6x2) * (6 + -4x + 2x2)
(3(6 + -4x + 2x2) + -7x * (6 + -4x + 2x2) + 6x2 * (6 + -4x + 2x2)) = 0
((6 * 3 + -4x * 3 + 2x2 * 3) + -7x * (6 + -4x + 2x2) + 6x2 * (6 + -4x + 2x2)) = 0
((18 + -12x + 6x2) + -7x * (6 + -4x + 2x2) + 6x2 * (6 + -4x + 2x2)) = 0
(18 + -12x + 6x2 + (6 * -7x + -4x * -7x + 2x2 * -7x) + 6x2 * (6 + -4x + 2x2)) = 0
(18 + -12x + 6x2 + (-42x + 28x2 + -14x3) + 6x2 * (6 + -4x + 2x2)) = 0
(18 + -12x + 6x2 + -42x + 28x2 + -14x3 + (6 * 6x2 + -4x * 6x2 + 2x2 * 6x2)) = 0
(18 + -12x + 6x2 + -42x + 28x2 + -14x3 + (36x2 + -24x3 + 12x4)) = 0

Reorder the terms:
(18 + -12x + -42x + 6x2 + 28x2 + 36x2 + -14x3 + -24x3 + 12x4) = 0

Combine like terms: -12x + -42x = -54x
(18 + -54x + 6x2 + 28x2 + 36x2 + -14x3 + -24x3 + 12x4) = 0

Combine like terms: 6x2 + 28x2 = 34x2
(18 + -54x + 34x2 + 36x2 + -14x3 + -24x3 + 12x4) = 0

Combine like terms: 34x2 + 36x2 = 70x2
(18 + -54x + 70x2 + -14x3 + -24x3 + 12x4) = 0

Combine like terms: -14x3 + -24x3 = -38x3
(18 + -54x + 70x2 + -38x3 + 12x4) = 0

Solving
18 + -54x + 70x2 + -38x3 + 12x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -27x + 35x2 + -19x3 + 6x4) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(9 + -27x + 35x2 + -19x3 + 6x4)' equal to zero and attempt to solve:

Simplifying
9 + -27x + 35x2 + -19x3 + 6x4 = 0

Solving
9 + -27x + 35x2 + -19x3 + 6x4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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