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

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


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

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

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

Multiply (-7 + 3x) * (7 + x)
6x(-7(7 + x) + 3x * (7 + x)) = 0
6x((7 * -7 + x * -7) + 3x * (7 + x)) = 0
6x((-49 + -7x) + 3x * (7 + x)) = 0
6x(-49 + -7x + (7 * 3x + x * 3x)) = 0
6x(-49 + -7x + (21x + 3x2)) = 0

Combine like terms: -7x + 21x = 14x
6x(-49 + 14x + 3x2) = 0
(-49 * 6x + 14x * 6x + 3x2 * 6x) = 0
(-294x + 84x2 + 18x3) = 0

Solving
-294x + 84x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-49 + 14x + 3x2) = 0

Factor a trinomial.
6x((-7 + -1x)(7 + -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 '(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, -7, 2.333333333}

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