(2x+y)(x+5y)=0

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Solution for (2x+y)(x+5y)=0 equation: 


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

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

Reorder the terms:
((10xy + 2x2) + y(x + 5y)) = 0
((10xy + 2x2) + y(x + 5y)) = 0
(10xy + 2x2 + (x * y + 5y * y)) = 0
(10xy + 2x2 + (xy + 5y2)) = 0

Reorder the terms:
(10xy + xy + 2x2 + 5y2) = 0

Combine like terms: 10xy + xy = 11xy
(11xy + 2x2 + 5y2) = 0

Solving
11xy + 2x2 + 5y2 = 0

Solving for variable 'x'.

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


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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y

Subproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve:

Simplifying
x + 5y = 0

Solving
x + 5y = 0

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

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

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

Simplifying
x = -5y
Solution
x = {-0.5y, -5y}

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