(6x-4y)(7x+8y)=0

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Solution for (6x-4y)(7x+8y)=0 equation: 


Simplifying
(6x + -4y)(7x + 8y) = 0

Multiply (6x + -4y) * (7x + 8y)
(6x * (7x + 8y) + -4y * (7x + 8y)) = 0
((7x * 6x + 8y * 6x) + -4y * (7x + 8y)) = 0

Reorder the terms:
((48xy + 42x2) + -4y * (7x + 8y)) = 0
((48xy + 42x2) + -4y * (7x + 8y)) = 0
(48xy + 42x2 + (7x * -4y + 8y * -4y)) = 0
(48xy + 42x2 + (-28xy + -32y2)) = 0

Reorder the terms:
(48xy + -28xy + 42x2 + -32y2) = 0

Combine like terms: 48xy + -28xy = 20xy
(20xy + 42x2 + -32y2) = 0

Solving
20xy + 42x2 + -32y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10xy + 21x2 + -16y2) = 0

Factor a trinomial.
2((3x + -2y)(7x + 8y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve:

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

Subproblem 2
Set the factor '(7x + 8y)' equal to zero and attempt to solve:

Simplifying
7x + 8y = 0

Solving
7x + 8y = 0

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

Add '-8y' to each side of the equation.
7x + 8y + -8y = 0 + -8y

Combine like terms: 8y + -8y = 0
7x + 0 = 0 + -8y
7x = 0 + -8y
Remove the zero:
7x = -8y

Divide each side by '7'.
x = -1.142857143y

Simplifying
x = -1.142857143y
Solution
x = {0.6666666667y, -1.142857143y}

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