3x(x-2)(x+4)(2x+1)(5-3x)=

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Solution for 3x(x-2)(x+4)(2x+1)(5-3x)= equation: 


Simplifying
3x(x + -2)(x + 4)(2x + 1)(5 + -3x) = 0

Reorder the terms:
3x(-2 + x)(x + 4)(2x + 1)(5 + -3x) = 0

Reorder the terms:
3x(-2 + x)(4 + x)(2x + 1)(5 + -3x) = 0

Reorder the terms:
3x(-2 + x)(4 + x)(1 + 2x)(5 + -3x) = 0

Multiply (-2 + x) * (4 + x)
3x(-2(4 + x) + x(4 + x))(1 + 2x)(5 + -3x) = 0
3x((4 * -2 + x * -2) + x(4 + x))(1 + 2x)(5 + -3x) = 0
3x((-8 + -2x) + x(4 + x))(1 + 2x)(5 + -3x) = 0
3x(-8 + -2x + (4 * x + x * x))(1 + 2x)(5 + -3x) = 0
3x(-8 + -2x + (4x + x2))(1 + 2x)(5 + -3x) = 0

Combine like terms: -2x + 4x = 2x
3x(-8 + 2x + x2)(1 + 2x)(5 + -3x) = 0

Multiply (-8 + 2x + x2) * (1 + 2x)
3x(-8(1 + 2x) + 2x * (1 + 2x) + x2(1 + 2x))(5 + -3x) = 0
3x((1 * -8 + 2x * -8) + 2x * (1 + 2x) + x2(1 + 2x))(5 + -3x) = 0
3x((-8 + -16x) + 2x * (1 + 2x) + x2(1 + 2x))(5 + -3x) = 0
3x(-8 + -16x + (1 * 2x + 2x * 2x) + x2(1 + 2x))(5 + -3x) = 0
3x(-8 + -16x + (2x + 4x2) + x2(1 + 2x))(5 + -3x) = 0
3x(-8 + -16x + 2x + 4x2 + (1 * x2 + 2x * x2))(5 + -3x) = 0
3x(-8 + -16x + 2x + 4x2 + (1x2 + 2x3))(5 + -3x) = 0

Combine like terms: -16x + 2x = -14x
3x(-8 + -14x + 4x2 + 1x2 + 2x3)(5 + -3x) = 0

Combine like terms: 4x2 + 1x2 = 5x2
3x(-8 + -14x + 5x2 + 2x3)(5 + -3x) = 0

Multiply (-8 + -14x + 5x2 + 2x3) * (5 + -3x)
3x(-8(5 + -3x) + -14x * (5 + -3x) + 5x2 * (5 + -3x) + 2x3 * (5 + -3x)) = 0
3x((5 * -8 + -3x * -8) + -14x * (5 + -3x) + 5x2 * (5 + -3x) + 2x3 * (5 + -3x)) = 0
3x((-40 + 24x) + -14x * (5 + -3x) + 5x2 * (5 + -3x) + 2x3 * (5 + -3x)) = 0
3x(-40 + 24x + (5 * -14x + -3x * -14x) + 5x2 * (5 + -3x) + 2x3 * (5 + -3x)) = 0
3x(-40 + 24x + (-70x + 42x2) + 5x2 * (5 + -3x) + 2x3 * (5 + -3x)) = 0
3x(-40 + 24x + -70x + 42x2 + (5 * 5x2 + -3x * 5x2) + 2x3 * (5 + -3x)) = 0
3x(-40 + 24x + -70x + 42x2 + (25x2 + -15x3) + 2x3 * (5 + -3x)) = 0
3x(-40 + 24x + -70x + 42x2 + 25x2 + -15x3 + (5 * 2x3 + -3x * 2x3)) = 0
3x(-40 + 24x + -70x + 42x2 + 25x2 + -15x3 + (10x3 + -6x4)) = 0

Combine like terms: 24x + -70x = -46x
3x(-40 + -46x + 42x2 + 25x2 + -15x3 + 10x3 + -6x4) = 0

Combine like terms: 42x2 + 25x2 = 67x2
3x(-40 + -46x + 67x2 + -15x3 + 10x3 + -6x4) = 0

Combine like terms: -15x3 + 10x3 = -5x3
3x(-40 + -46x + 67x2 + -5x3 + -6x4) = 0
(-40 * 3x + -46x * 3x + 67x2 * 3x + -5x3 * 3x + -6x4 * 3x) = 0
(-120x + -138x2 + 201x3 + -15x4 + -18x5) = 0

Solving
-120x + -138x2 + 201x3 + -15x4 + -18x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-40 + -46x + 67x2 + -5x3 + -6x4) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-40 + -46x + 67x2 + -5x3 + -6x4)' equal to zero and attempt to solve:

Simplifying
-40 + -46x + 67x2 + -5x3 + -6x4 = 0

Solving
-40 + -46x + 67x2 + -5x3 + -6x4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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