(6x+8y)(8x-5y)=0

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Solution for (6x+8y)(8x-5y)=0 equation: 


Simplifying
(6x + 8y)(8x + -5y) = 0

Multiply (6x + 8y) * (8x + -5y)
(6x * (8x + -5y) + 8y * (8x + -5y)) = 0
((8x * 6x + -5y * 6x) + 8y * (8x + -5y)) = 0

Reorder the terms:
((-30xy + 48x2) + 8y * (8x + -5y)) = 0
((-30xy + 48x2) + 8y * (8x + -5y)) = 0
(-30xy + 48x2 + (8x * 8y + -5y * 8y)) = 0
(-30xy + 48x2 + (64xy + -40y2)) = 0

Reorder the terms:
(-30xy + 64xy + 48x2 + -40y2) = 0

Combine like terms: -30xy + 64xy = 34xy
(34xy + 48x2 + -40y2) = 0

Solving
34xy + 48x2 + -40y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17xy + 24x2 + -20y2) = 0

Factor a trinomial.
2((8x + -5y)(3x + 4y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(8x + -5y)' equal to zero and attempt to solve:

Simplifying
8x + -5y = 0

Solving
8x + -5y = 0

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

Add '5y' to each side of the equation.
8x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
8x + 0 = 0 + 5y
8x = 0 + 5y
Remove the zero:
8x = 5y

Divide each side by '8'.
x = 0.625y

Simplifying
x = 0.625y

Subproblem 2
Set the factor '(3x + 4y)' equal to zero and attempt to solve:

Simplifying
3x + 4y = 0

Solving
3x + 4y = 0

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

Add '-4y' to each side of the equation.
3x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
3x + 0 = 0 + -4y
3x = 0 + -4y
Remove the zero:
3x = -4y

Divide each side by '3'.
x = -1.333333333y

Simplifying
x = -1.333333333y
Solution
x = {0.625y, -1.333333333y}

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