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

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


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

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

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

Multiply (-2 + 4x) * (-7 + 3x)
x(-2(-7 + 3x) + 4x * (-7 + 3x)) = 0
x((-7 * -2 + 3x * -2) + 4x * (-7 + 3x)) = 0
x((14 + -6x) + 4x * (-7 + 3x)) = 0
x(14 + -6x + (-7 * 4x + 3x * 4x)) = 0
x(14 + -6x + (-28x + 12x2)) = 0

Combine like terms: -6x + -28x = -34x
x(14 + -34x + 12x2) = 0
(14 * x + -34x * x + 12x2 * x) = 0
(14x + -34x2 + 12x3) = 0

Solving
14x + -34x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(7 + -17x + 6x2) = 0

Factor a trinomial.
2x((1 + -2x)(7 + -3x)) = 0

Ignore the factor 2.

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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 3
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
Solution
x = {0, 0.5, 2.333333333}

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