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

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


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

Reorder the terms:
(2x + y)(-1x + 4y) = 0

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

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

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

Combine like terms: 8xy + -1xy = 7xy
(7xy + -2x2 + 4y2) = 0

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

Solving for variable 'x'.

Factor a trinomial.
(-2x + -1y)(x + -4y) = 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 '(x + -4y)' equal to zero and attempt to solve:

Simplifying
x + -4y = 0

Solving
x + -4y = 0

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

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

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

Simplifying
x = 4y
Solution
x = {-0.5y, 4y}

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