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

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


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

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

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

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

Combine like terms: -8xy + xy = -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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