(2x+y)(4x+y)=0

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Solution for (2x+y)(4x+y)=0 equation: 


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

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

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

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

Combine like terms: 2xy + 4xy = 6xy
(6xy + 8x2 + y2) = 0

Solving
6xy + 8x2 + y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.25y, -0.5y}

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