6x(3x-2)(x+7)=0

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Solution for 6x(3x-2)(x+7)=0 equation: 


Simplifying
6x(3x + -2)(x + 7) = 0

Reorder the terms:
6x(-2 + 3x)(x + 7) = 0

Reorder the terms:
6x(-2 + 3x)(7 + x) = 0

Multiply (-2 + 3x) * (7 + x)
6x(-2(7 + x) + 3x * (7 + x)) = 0
6x((7 * -2 + x * -2) + 3x * (7 + x)) = 0
6x((-14 + -2x) + 3x * (7 + x)) = 0
6x(-14 + -2x + (7 * 3x + x * 3x)) = 0
6x(-14 + -2x + (21x + 3x2)) = 0

Combine like terms: -2x + 21x = 19x
6x(-14 + 19x + 3x2) = 0
(-14 * 6x + 19x * 6x + 3x2 * 6x) = 0
(-84x + 114x2 + 18x3) = 0

Solving
-84x + 114x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-14 + 19x + 3x2) = 0

Factor a trinomial.
6x((-7 + -1x)(2 + -3x)) = 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 '(-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

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, -7, 0.6666666667}

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