(6x+5y)(8x+7y)=0

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Solution for (6x+5y)(8x+7y)=0 equation: 


Simplifying
(6x + 5y)(8x + 7y) = 0

Multiply (6x + 5y) * (8x + 7y)
(6x * (8x + 7y) + 5y * (8x + 7y)) = 0
((8x * 6x + 7y * 6x) + 5y * (8x + 7y)) = 0

Reorder the terms:
((42xy + 48x2) + 5y * (8x + 7y)) = 0
((42xy + 48x2) + 5y * (8x + 7y)) = 0
(42xy + 48x2 + (8x * 5y + 7y * 5y)) = 0
(42xy + 48x2 + (40xy + 35y2)) = 0

Reorder the terms:
(42xy + 40xy + 48x2 + 35y2) = 0

Combine like terms: 42xy + 40xy = 82xy
(82xy + 48x2 + 35y2) = 0

Solving
82xy + 48x2 + 35y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6x + 5y)(8x + 7y) = 0


Subproblem 1
Set the factor '(6x + 5y)' equal to zero and attempt to solve:

Simplifying
6x + 5y = 0

Solving
6x + 5y = 0

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

Add '-5y' to each side of the equation.
6x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
6x + 0 = 0 + -5y
6x = 0 + -5y
Remove the zero:
6x = -5y

Divide each side by '6'.
x = -0.8333333333y

Simplifying
x = -0.8333333333y

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

Simplifying
8x + 7y = 0

Solving
8x + 7y = 0

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

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

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

Divide each side by '8'.
x = -0.875y

Simplifying
x = -0.875y
Solution
x = {-0.8333333333y, -0.875y}

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