(X+3)(2x-7)(4x)=0

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


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

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

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

Remove parenthesis around (4x)
(3 + X)(-7 + 2x) * 4x = 0

Reorder the terms for easier multiplication:
4x(3 + X)(-7 + 2x) = 0

Multiply (3 + X) * (-7 + 2x)
4x(3(-7 + 2x) + X(-7 + 2x)) = 0
4x((-7 * 3 + 2x * 3) + X(-7 + 2x)) = 0
4x((-21 + 6x) + X(-7 + 2x)) = 0
4x(-21 + 6x + (-7 * X + 2x * X)) = 0
4x(-21 + 6x + (-7X + 2xX)) = 0

Reorder the terms:
4x(-21 + -7X + 6x + 2xX) = 0
4x(-21 + -7X + 6x + 2xX) = 0
(-21 * 4x + -7X * 4x + 6x * 4x + 2xX * 4x) = 0
(-84x + -28xX + 24x2 + 8x2X) = 0

Solving
-84x + -28xX + 24x2 + 8x2X = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-21 + -7X + 6x + 2xX) = 0

Ignore the factor 4.

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 '(-21 + -7X + 6x + 2xX)' equal to zero and attempt to solve:

Simplifying
-21 + -7X + 6x + 2xX = 0

Solving
-21 + -7X + 6x + 2xX = 0

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

Add '21' to each side of the equation.
-21 + -7X + 6x + 21 + 2xX = 0 + 21

Reorder the terms:
-21 + 21 + -7X + 6x + 2xX = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -7X + 6x + 2xX = 0 + 21
-7X + 6x + 2xX = 0 + 21

Combine like terms: 0 + 21 = 21
-7X + 6x + 2xX = 21

Add '7X' to each side of the equation.
-7X + 6x + 7X + 2xX = 21 + 7X

Reorder the terms:
-7X + 7X + 6x + 2xX = 21 + 7X

Combine like terms: -7X + 7X = 0
0 + 6x + 2xX = 21 + 7X
6x + 2xX = 21 + 7X

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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