(4x-6)(3x^2+2x+1)=0

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Solution for (4x-6)(3x^2+2x+1)=0 equation: 


Simplifying
(4x + -6)(3x2 + 2x + 1) = 0

Reorder the terms:
(-6 + 4x)(3x2 + 2x + 1) = 0

Reorder the terms:
(-6 + 4x)(1 + 2x + 3x2) = 0

Multiply (-6 + 4x) * (1 + 2x + 3x2)
(-6(1 + 2x + 3x2) + 4x * (1 + 2x + 3x2)) = 0
((1 * -6 + 2x * -6 + 3x2 * -6) + 4x * (1 + 2x + 3x2)) = 0
((-6 + -12x + -18x2) + 4x * (1 + 2x + 3x2)) = 0
(-6 + -12x + -18x2 + (1 * 4x + 2x * 4x + 3x2 * 4x)) = 0
(-6 + -12x + -18x2 + (4x + 8x2 + 12x3)) = 0

Reorder the terms:
(-6 + -12x + 4x + -18x2 + 8x2 + 12x3) = 0

Combine like terms: -12x + 4x = -8x
(-6 + -8x + -18x2 + 8x2 + 12x3) = 0

Combine like terms: -18x2 + 8x2 = -10x2
(-6 + -8x + -10x2 + 12x3) = 0

Solving
-6 + -8x + -10x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -4x + -5x2 + 6x3) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -4x + -5x2 + 6x3)' equal to zero and attempt to solve:

Simplifying
-3 + -4x + -5x2 + 6x3 = 0

Solving
-3 + -4x + -5x2 + 6x3 = 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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