(9x-5y)(2x-7y)=0

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Solution for (9x-5y)(2x-7y)=0 equation: 


Simplifying
(9x + -5y)(2x + -7y) = 0

Multiply (9x + -5y) * (2x + -7y)
(9x * (2x + -7y) + -5y * (2x + -7y)) = 0
((2x * 9x + -7y * 9x) + -5y * (2x + -7y)) = 0

Reorder the terms:
((-63xy + 18x2) + -5y * (2x + -7y)) = 0
((-63xy + 18x2) + -5y * (2x + -7y)) = 0
(-63xy + 18x2 + (2x * -5y + -7y * -5y)) = 0
(-63xy + 18x2 + (-10xy + 35y2)) = 0

Reorder the terms:
(-63xy + -10xy + 18x2 + 35y2) = 0

Combine like terms: -63xy + -10xy = -73xy
(-73xy + 18x2 + 35y2) = 0

Solving
-73xy + 18x2 + 35y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -7y)(9x + -5y) = 0


Subproblem 1
Set the factor '(2x + -7y)' equal to zero and attempt to solve:

Simplifying
2x + -7y = 0

Solving
2x + -7y = 0

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

Add '7y' to each side of the equation.
2x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
2x + 0 = 0 + 7y
2x = 0 + 7y
Remove the zero:
2x = 7y

Divide each side by '2'.
x = 3.5y

Simplifying
x = 3.5y

Subproblem 2
Set the factor '(9x + -5y)' equal to zero and attempt to solve:

Simplifying
9x + -5y = 0

Solving
9x + -5y = 0

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

Add '5y' to each side of the equation.
9x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
9x + 0 = 0 + 5y
9x = 0 + 5y
Remove the zero:
9x = 5y

Divide each side by '9'.
x = 0.5555555556y

Simplifying
x = 0.5555555556y
Solution
x = {3.5y, 0.5555555556y}

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