(5x+y)(x+6y)=0

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Solution for (5x+y)(x+6y)=0 equation: 


Simplifying
(5x + y)(x + 6y) = 0

Multiply (5x + y) * (x + 6y)
(5x * (x + 6y) + y(x + 6y)) = 0
((x * 5x + 6y * 5x) + y(x + 6y)) = 0

Reorder the terms:
((30xy + 5x2) + y(x + 6y)) = 0
((30xy + 5x2) + y(x + 6y)) = 0
(30xy + 5x2 + (x * y + 6y * y)) = 0
(30xy + 5x2 + (xy + 6y2)) = 0

Reorder the terms:
(30xy + xy + 5x2 + 6y2) = 0

Combine like terms: 30xy + xy = 31xy
(31xy + 5x2 + 6y2) = 0

Solving
31xy + 5x2 + 6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + y)(x + 6y) = 0


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 + 6y)' equal to zero and attempt to solve:

Simplifying
x + 6y = 0

Solving
x + 6y = 0

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

Add '-6y' to each side of the equation.
x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
x + 0 = 0 + -6y
x = 0 + -6y
Remove the zero:
x = -6y

Simplifying
x = -6y
Solution
x = {-0.2y, -6y}

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