(7x+3y)(x+2y)=0

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Solution for (7x+3y)(x+2y)=0 equation: 


Simplifying
(7x + 3y)(x + 2y) = 0

Multiply (7x + 3y) * (x + 2y)
(7x * (x + 2y) + 3y * (x + 2y)) = 0
((x * 7x + 2y * 7x) + 3y * (x + 2y)) = 0

Reorder the terms:
((14xy + 7x2) + 3y * (x + 2y)) = 0
((14xy + 7x2) + 3y * (x + 2y)) = 0
(14xy + 7x2 + (x * 3y + 2y * 3y)) = 0
(14xy + 7x2 + (3xy + 6y2)) = 0

Reorder the terms:
(14xy + 3xy + 7x2 + 6y2) = 0

Combine like terms: 14xy + 3xy = 17xy
(17xy + 7x2 + 6y2) = 0

Solving
17xy + 7x2 + 6y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + 3y)(x + 2y) = 0


Subproblem 1
Set the factor '(7x + 3y)' equal to zero and attempt to solve:

Simplifying
7x + 3y = 0

Solving
7x + 3y = 0

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

Add '-3y' to each side of the equation.
7x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
7x + 0 = 0 + -3y
7x = 0 + -3y
Remove the zero:
7x = -3y

Divide each side by '7'.
x = -0.4285714286y

Simplifying
x = -0.4285714286y

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 = {-0.4285714286y, -2y}

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