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

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


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

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

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

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

Combine like terms: -1xy + -4xy = -5xy
2(-5xy + 2x2 + 2y2) = 0
(-5xy * 2 + 2x2 * 2 + 2y2 * 2) = 0
(-10xy + 4x2 + 4y2) = 0

Solving
-10xy + 4x2 + 4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5xy + 2x2 + 2y2) = 0

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

Ignore the factor 2.

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

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

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

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

Simplifying
x = 2y

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 = {2y, 0.5y}

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