(3x+y)(2x+4y)=

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Solution for (3x+y)(2x+4y)= equation: 


Simplifying
(3x + y)(2x + 4y) = 0

Multiply (3x + y) * (2x + 4y)
(3x * (2x + 4y) + y(2x + 4y)) = 0
((2x * 3x + 4y * 3x) + y(2x + 4y)) = 0

Reorder the terms:
((12xy + 6x2) + y(2x + 4y)) = 0
((12xy + 6x2) + y(2x + 4y)) = 0
(12xy + 6x2 + (2x * y + 4y * y)) = 0
(12xy + 6x2 + (2xy + 4y2)) = 0

Reorder the terms:
(12xy + 2xy + 6x2 + 4y2) = 0

Combine like terms: 12xy + 2xy = 14xy
(14xy + 6x2 + 4y2) = 0

Solving
14xy + 6x2 + 4y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7xy + 3x2 + 2y2) = 0

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

Ignore the factor 2.

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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