6(2-7x)x(7x-2)=0

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Solution for 6(2-7x)x(7x-2)=0 equation: 


Simplifying
6(2 + -7x) * x(7x + -2) = 0

Reorder the terms:
6(2 + -7x) * x(-2 + 7x) = 0

Reorder the terms for easier multiplication:
6x(2 + -7x)(-2 + 7x) = 0

Multiply (2 + -7x) * (-2 + 7x)
6x(2(-2 + 7x) + -7x * (-2 + 7x)) = 0
6x((-2 * 2 + 7x * 2) + -7x * (-2 + 7x)) = 0
6x((-4 + 14x) + -7x * (-2 + 7x)) = 0
6x(-4 + 14x + (-2 * -7x + 7x * -7x)) = 0
6x(-4 + 14x + (14x + -49x2)) = 0

Combine like terms: 14x + 14x = 28x
6x(-4 + 28x + -49x2) = 0
(-4 * 6x + 28x * 6x + -49x2 * 6x) = 0
(-24x + 168x2 + -294x3) = 0

Solving
-24x + 168x2 + -294x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-4 + 28x + -49x2) = 0

Factor a trinomial.
6x((-2 + 7x)(2 + -7x)) = 0

Ignore the factor 6.

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

Simplifying
-2 + 7x = 0

Solving
-2 + 7x = 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 + 7x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7x = 0 + 2
7x = 0 + 2

Combine like terms: 0 + 2 = 2
7x = 2

Divide each side by '7'.
x = 0.2857142857

Simplifying
x = 0.2857142857

Subproblem 3
Set the factor '(2 + -7x)' equal to zero and attempt to solve:

Simplifying
2 + -7x = 0

Solving
2 + -7x = 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 + -7x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7x = 0 + -2
-7x = 0 + -2

Combine like terms: 0 + -2 = -2
-7x = -2

Divide each side by '-7'.
x = 0.2857142857

Simplifying
x = 0.2857142857
Solution
x = {0, 0.2857142857, 0.2857142857}

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