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

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


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

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

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

Multiply (-3 + 4x) * (4 + 7x)
6(-3(4 + 7x) + 4x * (4 + 7x)) = 0
6((4 * -3 + 7x * -3) + 4x * (4 + 7x)) = 0
6((-12 + -21x) + 4x * (4 + 7x)) = 0
6(-12 + -21x + (4 * 4x + 7x * 4x)) = 0
6(-12 + -21x + (16x + 28x2)) = 0

Combine like terms: -21x + 16x = -5x
6(-12 + -5x + 28x2) = 0
(-12 * 6 + -5x * 6 + 28x2 * 6) = 0
(-72 + -30x + 168x2) = 0

Solving
-72 + -30x + 168x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + -5x + 28x2) = 0

Factor a trinomial.
6((-4 + -7x)(3 + -4x)) = 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 '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-0.5714285714, 0.75}

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