4x(3x-7)(7x+3)=0

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Solution for 4x(3x-7)(7x+3)=0 equation: 


Simplifying
4x(3x + -7)(7x + 3) = 0

Reorder the terms:
4x(-7 + 3x)(7x + 3) = 0

Reorder the terms:
4x(-7 + 3x)(3 + 7x) = 0

Multiply (-7 + 3x) * (3 + 7x)
4x(-7(3 + 7x) + 3x * (3 + 7x)) = 0
4x((3 * -7 + 7x * -7) + 3x * (3 + 7x)) = 0
4x((-21 + -49x) + 3x * (3 + 7x)) = 0
4x(-21 + -49x + (3 * 3x + 7x * 3x)) = 0
4x(-21 + -49x + (9x + 21x2)) = 0

Combine like terms: -49x + 9x = -40x
4x(-21 + -40x + 21x2) = 0
(-21 * 4x + -40x * 4x + 21x2 * 4x) = 0
(-84x + -160x2 + 84x3) = 0

Solving
-84x + -160x2 + 84x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-21 + -40x + 21x2) = 0

Factor a trinomial.
4x((-3 + -7x)(7 + -3x)) = 0

Ignore the factor 4.

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 '(-3 + -7x)' equal to zero and attempt to solve:

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + -7x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7x = 0 + 3
-7x = 0 + 3

Combine like terms: 0 + 3 = 3
-7x = 3

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286

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, -0.4285714286, 2.333333333}

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