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

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


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

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

Reorder the terms:
((-49xy + 56x2) + -6y * (8x + -7y)) = 0
((-49xy + 56x2) + -6y * (8x + -7y)) = 0
(-49xy + 56x2 + (8x * -6y + -7y * -6y)) = 0
(-49xy + 56x2 + (-48xy + 42y2)) = 0

Reorder the terms:
(-49xy + -48xy + 56x2 + 42y2) = 0

Combine like terms: -49xy + -48xy = -97xy
(-97xy + 56x2 + 42y2) = 0

Solving
-97xy + 56x2 + 42y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(7x + -6y)' equal to zero and attempt to solve:

Simplifying
7x + -6y = 0

Solving
7x + -6y = 0

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

Add '6y' to each side of the equation.
7x + -6y + 6y = 0 + 6y

Combine like terms: -6y + 6y = 0
7x + 0 = 0 + 6y
7x = 0 + 6y
Remove the zero:
7x = 6y

Divide each side by '7'.
x = 0.8571428571y

Simplifying
x = 0.8571428571y
Solution
x = {0.875y, 0.8571428571y}

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