6(3x-7)(7x+4)=0

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Solution for 6(3x-7)(7x+4)=0 equation: 


Simplifying
6(3x + -7)(7x + 4) = 0

Reorder the terms:
6(-7 + 3x)(7x + 4) = 0

Reorder the terms:
6(-7 + 3x)(4 + 7x) = 0

Multiply (-7 + 3x) * (4 + 7x)
6(-7(4 + 7x) + 3x * (4 + 7x)) = 0
6((4 * -7 + 7x * -7) + 3x * (4 + 7x)) = 0
6((-28 + -49x) + 3x * (4 + 7x)) = 0
6(-28 + -49x + (4 * 3x + 7x * 3x)) = 0
6(-28 + -49x + (12x + 21x2)) = 0

Combine like terms: -49x + 12x = -37x
6(-28 + -37x + 21x2) = 0
(-28 * 6 + -37x * 6 + 21x2 * 6) = 0
(-168 + -222x + 126x2) = 0

Solving
-168 + -222x + 126x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-28 + -37x + 21x2) = 0

Factor a trinomial.
6((-4 + -7x)(7 + -3x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-4 + -7x)' equal to zero and attempt to solve:

Simplifying
-4 + -7x = 0

Solving
-4 + -7x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7x = 0 + 4
-7x = 0 + 4

Combine like terms: 0 + 4 = 4
-7x = 4

Divide each side by '-7'.
x = -0.5714285714

Simplifying
x = -0.5714285714

Subproblem 2
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 = {-0.5714285714, 2.333333333}

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