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

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


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

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

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

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

Combine like terms: xy + -8xy = -7xy
(-7xy + 4x2 + -2y2) = 0

Solving
-7xy + 4x2 + -2y2 = 0

Solving for variable 'x'.

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


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 '(4x + y)' equal to zero and attempt to solve:

Simplifying
4x + y = 0

Solving
4x + y = 0

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

Add '-1y' to each side of the equation.
4x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
4x + 0 = 0 + -1y
4x = 0 + -1y
Remove the zero:
4x = -1y

Divide each side by '4'.
x = -0.25y

Simplifying
x = -0.25y
Solution
x = {2y, -0.25y}

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