6(7x-4)(3x+5)=0

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Solution for 6(7x-4)(3x+5)=0 equation: 


Simplifying
6(7x + -4)(3x + 5) = 0

Reorder the terms:
6(-4 + 7x)(3x + 5) = 0

Reorder the terms:
6(-4 + 7x)(5 + 3x) = 0

Multiply (-4 + 7x) * (5 + 3x)
6(-4(5 + 3x) + 7x * (5 + 3x)) = 0
6((5 * -4 + 3x * -4) + 7x * (5 + 3x)) = 0
6((-20 + -12x) + 7x * (5 + 3x)) = 0
6(-20 + -12x + (5 * 7x + 3x * 7x)) = 0
6(-20 + -12x + (35x + 21x2)) = 0

Combine like terms: -12x + 35x = 23x
6(-20 + 23x + 21x2) = 0
(-20 * 6 + 23x * 6 + 21x2 * 6) = 0
(-120 + 138x + 126x2) = 0

Solving
-120 + 138x + 126x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-20 + 23x + 21x2) = 0

Factor a trinomial.
6((-5 + -3x)(4 + -7x)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 2
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
Solution
x = {-1.666666667, 0.5714285714}

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