(3x-2)x(7x+1)=0

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Solution for (3x-2)x(7x+1)=0 equation: 


Simplifying
(3x + -2) * x(7x + 1) = 0

Reorder the terms:
(-2 + 3x) * x(7x + 1) = 0

Reorder the terms:
(-2 + 3x) * x(1 + 7x) = 0

Reorder the terms for easier multiplication:
x(-2 + 3x)(1 + 7x) = 0

Multiply (-2 + 3x) * (1 + 7x)
x(-2(1 + 7x) + 3x * (1 + 7x)) = 0
x((1 * -2 + 7x * -2) + 3x * (1 + 7x)) = 0
x((-2 + -14x) + 3x * (1 + 7x)) = 0
x(-2 + -14x + (1 * 3x + 7x * 3x)) = 0
x(-2 + -14x + (3x + 21x2)) = 0

Combine like terms: -14x + 3x = -11x
x(-2 + -11x + 21x2) = 0
(-2 * x + -11x * x + 21x2 * x) = 0
(-2x + -11x2 + 21x3) = 0

Solving
-2x + -11x2 + 21x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + -11x + 21x2) = 0

Factor a trinomial.
x((-1 + -7x)(2 + -3x)) = 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 '(-1 + -7x)' equal to zero and attempt to solve:

Simplifying
-1 + -7x = 0

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

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

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

Divide each side by '-7'.
x = -0.1428571429

Simplifying
x = -0.1428571429

Subproblem 3
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
Solution
x = {0, -0.1428571429, 0.6666666667}

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