(-5x+y)(2x-4y)=

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Solution for (-5x+y)(2x-4y)= equation: 


Simplifying
(-5x + y)(2x + -4y) = 0

Multiply (-5x + y) * (2x + -4y)
(-5x * (2x + -4y) + y(2x + -4y)) = 0
((2x * -5x + -4y * -5x) + y(2x + -4y)) = 0

Reorder the terms:
((20xy + -10x2) + y(2x + -4y)) = 0
((20xy + -10x2) + y(2x + -4y)) = 0
(20xy + -10x2 + (2x * y + -4y * y)) = 0
(20xy + -10x2 + (2xy + -4y2)) = 0

Reorder the terms:
(20xy + 2xy + -10x2 + -4y2) = 0

Combine like terms: 20xy + 2xy = 22xy
(22xy + -10x2 + -4y2) = 0

Solving
22xy + -10x2 + -4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(11xy + -5x2 + -2y2) = 0

Factor a trinomial.
2((-5x + y)(x + -2y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5x + y)' equal to zero and attempt to solve:

Simplifying
-5x + y = 0

Solving
-5x + y = 0

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

Add '-1y' to each side of the equation.
-5x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
-5x + 0 = 0 + -1y
-5x = 0 + -1y
Remove the zero:
-5x = -1y

Divide each side by '-5'.
x = 0.2y

Simplifying
x = 0.2y

Subproblem 2
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
Solution
x = {0.2y, 2y}

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