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

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


Simplifying
(4x + y)(2x + -1y) = 0

Multiply (4x + y) * (2x + -1y)
(4x * (2x + -1y) + y(2x + -1y)) = 0
((2x * 4x + -1y * 4x) + y(2x + -1y)) = 0

Reorder the terms:
((-4xy + 8x2) + y(2x + -1y)) = 0
((-4xy + 8x2) + y(2x + -1y)) = 0
(-4xy + 8x2 + (2x * y + -1y * y)) = 0
(-4xy + 8x2 + (2xy + -1y2)) = 0

Reorder the terms:
(-4xy + 2xy + 8x2 + -1y2) = 0

Combine like terms: -4xy + 2xy = -2xy
(-2xy + 8x2 + -1y2) = 0

Solving
-2xy + 8x2 + -1y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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 = {0.5y, -0.25y}

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