(A-B)(4A-2B)=

Solution for (A-B)(4A-2B)= equation:

Simplifying
(A + -1B)(4A + -2B) = 0

Multiply (A + -1B) * (4A + -2B)
(A(4A + -2B) + -1B * (4A + -2B)) = 0
((4A * A + -2B * A) + -1B * (4A + -2B)) = 0

Reorder the terms:
((-2AB + 4A2) + -1B * (4A + -2B)) = 0
((-2AB + 4A2) + -1B * (4A + -2B)) = 0
(-2AB + 4A2 + (4A * -1B + -2B * -1B)) = 0
(-2AB + 4A2 + (-4AB + 2B2)) = 0

Reorder the terms:
(-2AB + -4AB + 4A2 + 2B2) = 0

Combine like terms: -2AB + -4AB = -6AB
(-6AB + 4A2 + 2B2) = 0

Solving
-6AB + 4A2 + 2B2 = 0

Solving for variable 'A'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3AB + 2A2 + B2) = 0

Factor a trinomial.
2((A + -1B)(2A + -1B)) = 0

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

Simplifying
A + -1B = 0

Solving
A + -1B = 0

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

Add 'B' to each side of the equation.
A + -1B + B = 0 + B

Combine like terms: -1B + B = 0
A + 0 = 0 + B
A = 0 + B
Remove the zero:
A = B

Simplifying
A = B
Subproblem 2
Set the factor '(2A + -1B)' equal to zero and attempt to solve:

Simplifying
2A + -1B = 0

Solving
2A + -1B = 0

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

Add 'B' to each side of the equation.
2A + -1B + B = 0 + B

Combine like terms: -1B + B = 0
2A + 0 = 0 + B
2A = 0 + B
Remove the zero:
2A = B

Divide each side by '2'.
A = 0.5B

Simplifying
A = 0.5B
Solution
A = {B, 0.5B}