(x+2y)(3x+y)=

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Solution for (x+2y)(3x+y)= equation: 


Simplifying
(x + 2y)(3x + y) = 0

Multiply (x + 2y) * (3x + y)
(x(3x + y) + 2y * (3x + y)) = 0
((3x * x + y * x) + 2y * (3x + y)) = 0

Reorder the terms:
((xy + 3x2) + 2y * (3x + y)) = 0
((xy + 3x2) + 2y * (3x + y)) = 0
(xy + 3x2 + (3x * 2y + y * 2y)) = 0
(xy + 3x2 + (6xy + 2y2)) = 0

Reorder the terms:
(xy + 6xy + 3x2 + 2y2) = 0

Combine like terms: xy + 6xy = 7xy
(7xy + 3x2 + 2y2) = 0

Solving
7xy + 3x2 + 2y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + y)(x + 2y) = 0


Subproblem 1
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

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 = {-0.3333333333y, -2y}

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