(15x^3-2x^2+10x+12)(3x+2)=5x^2-4x+6

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Solution for (15x^3-2x^2+10x+12)(3x+2)=5x^2-4x+6 equation: 


Simplifying
(15x3 + -2x2 + 10x + 12)(3x + 2) = 5x2 + -4x + 6

Reorder the terms:
(12 + 10x + -2x2 + 15x3)(3x + 2) = 5x2 + -4x + 6

Reorder the terms:
(12 + 10x + -2x2 + 15x3)(2 + 3x) = 5x2 + -4x + 6

Multiply (12 + 10x + -2x2 + 15x3) * (2 + 3x)
(12(2 + 3x) + 10x * (2 + 3x) + -2x2 * (2 + 3x) + 15x3 * (2 + 3x)) = 5x2 + -4x + 6
((2 * 12 + 3x * 12) + 10x * (2 + 3x) + -2x2 * (2 + 3x) + 15x3 * (2 + 3x)) = 5x2 + -4x + 6
((24 + 36x) + 10x * (2 + 3x) + -2x2 * (2 + 3x) + 15x3 * (2 + 3x)) = 5x2 + -4x + 6
(24 + 36x + (2 * 10x + 3x * 10x) + -2x2 * (2 + 3x) + 15x3 * (2 + 3x)) = 5x2 + -4x + 6
(24 + 36x + (20x + 30x2) + -2x2 * (2 + 3x) + 15x3 * (2 + 3x)) = 5x2 + -4x + 6
(24 + 36x + 20x + 30x2 + (2 * -2x2 + 3x * -2x2) + 15x3 * (2 + 3x)) = 5x2 + -4x + 6
(24 + 36x + 20x + 30x2 + (-4x2 + -6x3) + 15x3 * (2 + 3x)) = 5x2 + -4x + 6
(24 + 36x + 20x + 30x2 + -4x2 + -6x3 + (2 * 15x3 + 3x * 15x3)) = 5x2 + -4x + 6
(24 + 36x + 20x + 30x2 + -4x2 + -6x3 + (30x3 + 45x4)) = 5x2 + -4x + 6

Combine like terms: 36x + 20x = 56x
(24 + 56x + 30x2 + -4x2 + -6x3 + 30x3 + 45x4) = 5x2 + -4x + 6

Combine like terms: 30x2 + -4x2 = 26x2
(24 + 56x + 26x2 + -6x3 + 30x3 + 45x4) = 5x2 + -4x + 6

Combine like terms: -6x3 + 30x3 = 24x3
(24 + 56x + 26x2 + 24x3 + 45x4) = 5x2 + -4x + 6

Reorder the terms:
24 + 56x + 26x2 + 24x3 + 45x4 = 6 + -4x + 5x2

Solving
24 + 56x + 26x2 + 24x3 + 45x4 = 6 + -4x + 5x2

Solving for variable 'x'.

Reorder the terms:
24 + -6 + 56x + 4x + 26x2 + -5x2 + 24x3 + 45x4 = 6 + -4x + 5x2 + -6 + 4x + -5x2

Combine like terms: 24 + -6 = 18
18 + 56x + 4x + 26x2 + -5x2 + 24x3 + 45x4 = 6 + -4x + 5x2 + -6 + 4x + -5x2

Combine like terms: 56x + 4x = 60x
18 + 60x + 26x2 + -5x2 + 24x3 + 45x4 = 6 + -4x + 5x2 + -6 + 4x + -5x2

Combine like terms: 26x2 + -5x2 = 21x2
18 + 60x + 21x2 + 24x3 + 45x4 = 6 + -4x + 5x2 + -6 + 4x + -5x2

Reorder the terms:
18 + 60x + 21x2 + 24x3 + 45x4 = 6 + -6 + -4x + 4x + 5x2 + -5x2

Combine like terms: 6 + -6 = 0
18 + 60x + 21x2 + 24x3 + 45x4 = 0 + -4x + 4x + 5x2 + -5x2
18 + 60x + 21x2 + 24x3 + 45x4 = -4x + 4x + 5x2 + -5x2

Combine like terms: -4x + 4x = 0
18 + 60x + 21x2 + 24x3 + 45x4 = 0 + 5x2 + -5x2
18 + 60x + 21x2 + 24x3 + 45x4 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
18 + 60x + 21x2 + 24x3 + 45x4 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 20x + 7x2 + 8x3 + 15x4) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(6 + 20x + 7x2 + 8x3 + 15x4)' equal to zero and attempt to solve:

Simplifying
6 + 20x + 7x2 + 8x3 + 15x4 = 0

Solving
6 + 20x + 7x2 + 8x3 + 15x4 = 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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