(6x+-4y)(5x+-3y)=0

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Solution for (6x+-4y)(5x+-3y)=0 equation: 


Simplifying
(6x + -4y)(5x + -3y) = 0

Multiply (6x + -4y) * (5x + -3y)
(6x * (5x + -3y) + -4y * (5x + -3y)) = 0
((5x * 6x + -3y * 6x) + -4y * (5x + -3y)) = 0

Reorder the terms:
((-18xy + 30x2) + -4y * (5x + -3y)) = 0
((-18xy + 30x2) + -4y * (5x + -3y)) = 0
(-18xy + 30x2 + (5x * -4y + -3y * -4y)) = 0
(-18xy + 30x2 + (-20xy + 12y2)) = 0

Reorder the terms:
(-18xy + -20xy + 30x2 + 12y2) = 0

Combine like terms: -18xy + -20xy = -38xy
(-38xy + 30x2 + 12y2) = 0

Solving
-38xy + 30x2 + 12y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-19xy + 15x2 + 6y2) = 0

Factor a trinomial.
2((3x + -2y)(5x + -3y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve:

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y

Subproblem 2
Set the factor '(5x + -3y)' equal to zero and attempt to solve:

Simplifying
5x + -3y = 0

Solving
5x + -3y = 0

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

Add '3y' to each side of the equation.
5x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
5x + 0 = 0 + 3y
5x = 0 + 3y
Remove the zero:
5x = 3y

Divide each side by '5'.
x = 0.6y

Simplifying
x = 0.6y
Solution
x = {0.6666666667y, 0.6y}

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