(2x-7y)(6x-5y)=0

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Solution for (2x-7y)(6x-5y)=0 equation: 


Simplifying
(2x + -7y)(6x + -5y) = 0

Multiply (2x + -7y) * (6x + -5y)
(2x * (6x + -5y) + -7y * (6x + -5y)) = 0
((6x * 2x + -5y * 2x) + -7y * (6x + -5y)) = 0

Reorder the terms:
((-10xy + 12x2) + -7y * (6x + -5y)) = 0
((-10xy + 12x2) + -7y * (6x + -5y)) = 0
(-10xy + 12x2 + (6x * -7y + -5y * -7y)) = 0
(-10xy + 12x2 + (-42xy + 35y2)) = 0

Reorder the terms:
(-10xy + -42xy + 12x2 + 35y2) = 0

Combine like terms: -10xy + -42xy = -52xy
(-52xy + 12x2 + 35y2) = 0

Solving
-52xy + 12x2 + 35y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -7y)(6x + -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 '(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
Solution
x = {3.5y, 0.8333333333y}

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