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

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

Simplifying
(x + -1y)(6x + 4y) = 0

Multiply (x + -1y) * (6x + 4y)
(x(6x + 4y) + -1y * (6x + 4y)) = 0
((6x * x + 4y * x) + -1y * (6x + 4y)) = 0

Reorder the terms:
((4xy + 6x2) + -1y * (6x + 4y)) = 0
((4xy + 6x2) + -1y * (6x + 4y)) = 0
(4xy + 6x2 + (6x * -1y + 4y * -1y)) = 0
(4xy + 6x2 + (-6xy + -4y2)) = 0

Reorder the terms:
(4xy + -6xy + 6x2 + -4y2) = 0

Combine like terms: 4xy + -6xy = -2xy
(-2xy + 6x2 + -4y2) = 0

Solving
-2xy + 6x2 + -4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1xy + 3x2 + -2y2) = 0

Factor a trinomial.
2((x + -1y)(3x + 2y)) = 0

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

Simplifying
x + -1y = 0

Solving
x + -1y = 0

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

Add 'y' to each side of the equation.
x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
x + 0 = 0 + y
x = 0 + y
Remove the zero:
x = y

Simplifying
x = y
Subproblem 2
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
Solution
x = {y, -0.6666666667y}