(6y+5x)(7y-9x)=0

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Solution for (6y+5x)(7y-9x)=0 equation: 


Simplifying
(6y + 5x)(7y + -9x) = 0

Reorder the terms:
(5x + 6y)(7y + -9x) = 0

Reorder the terms:
(5x + 6y)(-9x + 7y) = 0

Multiply (5x + 6y) * (-9x + 7y)
(5x * (-9x + 7y) + 6y * (-9x + 7y)) = 0
((-9x * 5x + 7y * 5x) + 6y * (-9x + 7y)) = 0

Reorder the terms:
((35xy + -45x2) + 6y * (-9x + 7y)) = 0
((35xy + -45x2) + 6y * (-9x + 7y)) = 0
(35xy + -45x2 + (-9x * 6y + 7y * 6y)) = 0
(35xy + -45x2 + (-54xy + 42y2)) = 0

Reorder the terms:
(35xy + -54xy + -45x2 + 42y2) = 0

Combine like terms: 35xy + -54xy = -19xy
(-19xy + -45x2 + 42y2) = 0

Solving
-19xy + -45x2 + 42y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5x + -6y)(9x + -7y) = 0


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

Simplifying
-5x + -6y = 0

Solving
-5x + -6y = 0

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

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

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

Divide each side by '-5'.
x = -1.2y

Simplifying
x = -1.2y

Subproblem 2
Set the factor '(9x + -7y)' equal to zero and attempt to solve:

Simplifying
9x + -7y = 0

Solving
9x + -7y = 0

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

Add '7y' to each side of the equation.
9x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
9x + 0 = 0 + 7y
9x = 0 + 7y
Remove the zero:
9x = 7y

Divide each side by '9'.
x = 0.7777777778y

Simplifying
x = 0.7777777778y
Solution
x = {-1.2y, 0.7777777778y}

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