(9x-2y)(4x-3y)=0

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Solution for (9x-2y)(4x-3y)=0 equation: 


Simplifying
(9x + -2y)(4x + -3y) = 0

Multiply (9x + -2y) * (4x + -3y)
(9x * (4x + -3y) + -2y * (4x + -3y)) = 0
((4x * 9x + -3y * 9x) + -2y * (4x + -3y)) = 0

Reorder the terms:
((-27xy + 36x2) + -2y * (4x + -3y)) = 0
((-27xy + 36x2) + -2y * (4x + -3y)) = 0
(-27xy + 36x2 + (4x * -2y + -3y * -2y)) = 0
(-27xy + 36x2 + (-8xy + 6y2)) = 0

Reorder the terms:
(-27xy + -8xy + 36x2 + 6y2) = 0

Combine like terms: -27xy + -8xy = -35xy
(-35xy + 36x2 + 6y2) = 0

Solving
-35xy + 36x2 + 6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -3y)(9x + -2y) = 0


Subproblem 1
Set the factor '(4x + -3y)' equal to zero and attempt to solve:

Simplifying
4x + -3y = 0

Solving
4x + -3y = 0

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

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

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

Divide each side by '4'.
x = 0.75y

Simplifying
x = 0.75y

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

Simplifying
9x + -2y = 0

Solving
9x + -2y = 0

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

Add '2y' to each side of the equation.
9x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
9x + 0 = 0 + 2y
9x = 0 + 2y
Remove the zero:
9x = 2y

Divide each side by '9'.
x = 0.2222222222y

Simplifying
x = 0.2222222222y
Solution
x = {0.75y, 0.2222222222y}

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