(3x-4y)(2x-7y)=0

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Solution for (3x-4y)(2x-7y)=0 equation: 


Simplifying
(3x + -4y)(2x + -7y) = 0

Multiply (3x + -4y) * (2x + -7y)
(3x * (2x + -7y) + -4y * (2x + -7y)) = 0
((2x * 3x + -7y * 3x) + -4y * (2x + -7y)) = 0

Reorder the terms:
((-21xy + 6x2) + -4y * (2x + -7y)) = 0
((-21xy + 6x2) + -4y * (2x + -7y)) = 0
(-21xy + 6x2 + (2x * -4y + -7y * -4y)) = 0
(-21xy + 6x2 + (-8xy + 28y2)) = 0

Reorder the terms:
(-21xy + -8xy + 6x2 + 28y2) = 0

Combine like terms: -21xy + -8xy = -29xy
(-29xy + 6x2 + 28y2) = 0

Solving
-29xy + 6x2 + 28y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + -7y)(3x + -4y) = 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 '(3x + -4y)' equal to zero and attempt to solve:

Simplifying
3x + -4y = 0

Solving
3x + -4y = 0

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

Add '4y' to each side of the equation.
3x + -4y + 4y = 0 + 4y

Combine like terms: -4y + 4y = 0
3x + 0 = 0 + 4y
3x = 0 + 4y
Remove the zero:
3x = 4y

Divide each side by '3'.
x = 1.333333333y

Simplifying
x = 1.333333333y
Solution
x = {3.5y, 1.333333333y}

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