(3x-7)(x-4)x=0

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


Simplifying
(3x + -7)(x + -4) * x = 0

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

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

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

Multiply (-7 + 3x) * (-4 + x)
x(-7(-4 + x) + 3x * (-4 + x)) = 0
x((-4 * -7 + x * -7) + 3x * (-4 + x)) = 0
x((28 + -7x) + 3x * (-4 + x)) = 0
x(28 + -7x + (-4 * 3x + x * 3x)) = 0
x(28 + -7x + (-12x + 3x2)) = 0

Combine like terms: -7x + -12x = -19x
x(28 + -19x + 3x2) = 0
(28 * x + -19x * x + 3x2 * x) = 0
(28x + -19x2 + 3x3) = 0

Solving
28x + -19x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(28 + -19x + 3x2) = 0

Factor a trinomial.
x((7 + -3x)(4 + -1x)) = 0


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 '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 2.333333333, 4}

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