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

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Solution for (4x-4y)(2x+y)=0 equation: 


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

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

Reorder the terms:
((4xy + 8x2) + -4y * (2x + y)) = 0
((4xy + 8x2) + -4y * (2x + y)) = 0
(4xy + 8x2 + (2x * -4y + y * -4y)) = 0
(4xy + 8x2 + (-8xy + -4y2)) = 0

Reorder the terms:
(4xy + -8xy + 8x2 + -4y2) = 0

Combine like terms: 4xy + -8xy = -4xy
(-4xy + 8x2 + -4y2) = 0

Solving
-4xy + 8x2 + -4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1xy + 2x2 + -1y2) = 0

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

Ignore the factor 4.

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 + y)' equal to zero and attempt to solve:

Simplifying
2x + y = 0

Solving
2x + y = 0

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

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

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

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

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

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