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

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

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

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

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

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

Combine like terms: -6xy + 4xy = -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((-1x + -1y)(3x + -2y)) = 0

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

Simplifying
-1x + -1y = 0

Solving
-1x + -1y = 0

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

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

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

Divide each side by '-1'.
x = -1y

Simplifying
x = -1y
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 = {-1y, 0.6666666667y}