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

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


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

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

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

Multiply (-7 + x) * (2 + 7x)
3x(-7(2 + 7x) + x(2 + 7x)) = 0
3x((2 * -7 + 7x * -7) + x(2 + 7x)) = 0
3x((-14 + -49x) + x(2 + 7x)) = 0
3x(-14 + -49x + (2 * x + 7x * x)) = 0
3x(-14 + -49x + (2x + 7x2)) = 0

Combine like terms: -49x + 2x = -47x
3x(-14 + -47x + 7x2) = 0
(-14 * 3x + -47x * 3x + 7x2 * 3x) = 0
(-42x + -141x2 + 21x3) = 0

Solving
-42x + -141x2 + 21x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-14 + -47x + 7x2) = 0

Factor a trinomial.
3x((-2 + -7x)(7 + -1x)) = 0

Ignore the factor 3.

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 '(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, -0.2857142857, 7}

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