(4x-2y)(x-y)=

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

Simplifying
(4x + -2y)(x + -1y) = 0

Multiply (4x + -2y) * (x + -1y)
(4x * (x + -1y) + -2y * (x + -1y)) = 0
((x * 4x + -1y * 4x) + -2y * (x + -1y)) = 0

Reorder the terms:
((-4xy + 4x2) + -2y * (x + -1y)) = 0
((-4xy + 4x2) + -2y * (x + -1y)) = 0
(-4xy + 4x2 + (x * -2y + -1y * -2y)) = 0
(-4xy + 4x2 + (-2xy + 2y2)) = 0

Reorder the terms:
(-4xy + -2xy + 4x2 + 2y2) = 0

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

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

Solving for variable 'x'.

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

Factor a trinomial.
2((x + -1y)(2x + -1y)) = 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 '(2x + -1y)' equal to zero and attempt to solve:

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

Add 'y' to each side of the equation.
2x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y
Solution
x = {y, 0.5y}