(3x+y)(x+-6y)=

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Solution for (3x+y)(x+-6y)= equation: 


Simplifying
(3x + y)(x + -6y) = 0

Multiply (3x + y) * (x + -6y)
(3x * (x + -6y) + y(x + -6y)) = 0
((x * 3x + -6y * 3x) + y(x + -6y)) = 0

Reorder the terms:
((-18xy + 3x2) + y(x + -6y)) = 0
((-18xy + 3x2) + y(x + -6y)) = 0
(-18xy + 3x2 + (x * y + -6y * y)) = 0
(-18xy + 3x2 + (xy + -6y2)) = 0

Reorder the terms:
(-18xy + xy + 3x2 + -6y2) = 0

Combine like terms: -18xy + xy = -17xy
(-17xy + 3x2 + -6y2) = 0

Solving
-17xy + 3x2 + -6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -6y)(3x + y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(3x + y)' equal to zero and attempt to solve:

Simplifying
3x + y = 0

Solving
3x + y = 0

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

Add '-1y' to each side of the equation.
3x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y
Solution
x = {6y, -0.3333333333y}

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