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

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


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

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

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

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

Reorder the terms:
(2x + -1xy + 4x2 + (-16xy + -8y + 4y2)) + 2(4y + -1x) = 0
(2x + -1xy + 4x2 + (-16xy + -8y + 4y2)) + 2(4y + -1x) = 0

Reorder the terms:
(2x + -1xy + -16xy + 4x2 + -8y + 4y2) + 2(4y + -1x) = 0

Combine like terms: -1xy + -16xy = -17xy
(2x + -17xy + 4x2 + -8y + 4y2) + 2(4y + -1x) = 0

Reorder the terms:
2x + -17xy + 4x2 + -8y + 4y2 + 2(-1x + 4y) = 0
2x + -17xy + 4x2 + -8y + 4y2 + (-1x * 2 + 4y * 2) = 0
2x + -17xy + 4x2 + -8y + 4y2 + (-2x + 8y) = 0

Reorder the terms:
2x + -2x + -17xy + 4x2 + -8y + 8y + 4y2 = 0

Combine like terms: 2x + -2x = 0
0 + -17xy + 4x2 + -8y + 8y + 4y2 = 0
-17xy + 4x2 + -8y + 8y + 4y2 = 0

Combine like terms: -8y + 8y = 0
-17xy + 4x2 + 0 + 4y2 = 0
-17xy + 4x2 + 4y2 = 0

Solving
-17xy + 4x2 + 4y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(4x + -1y)' equal to zero and attempt to solve:

Simplifying
4x + -1y = 0

Solving
4x + -1y = 0

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

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

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

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

Simplifying
x = 0.25y
Solution
x = {4y, 0.25y}

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