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

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


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

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

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

Multiply (-2 + 3x) * (-7 + x)
x(-2(-7 + x) + 3x * (-7 + x)) = 0
x((-7 * -2 + x * -2) + 3x * (-7 + x)) = 0
x((14 + -2x) + 3x * (-7 + x)) = 0
x(14 + -2x + (-7 * 3x + x * 3x)) = 0
x(14 + -2x + (-21x + 3x2)) = 0

Combine like terms: -2x + -21x = -23x
x(14 + -23x + 3x2) = 0
(14 * x + -23x * x + 3x2 * x) = 0
(14x + -23x2 + 3x3) = 0

Solving
14x + -23x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(14 + -23x + 3x2) = 0

Factor a trinomial.
x((2 + -3x)(7 + -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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 3
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {0, 0.6666666667, 7}

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