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

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


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

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

Reorder the terms:
((2xy + 7x2) + 3y * (7x + 2y)) = 0
((2xy + 7x2) + 3y * (7x + 2y)) = 0
(2xy + 7x2 + (7x * 3y + 2y * 3y)) = 0
(2xy + 7x2 + (21xy + 6y2)) = 0

Reorder the terms:
(2xy + 21xy + 7x2 + 6y2) = 0

Combine like terms: 2xy + 21xy = 23xy
(23xy + 7x2 + 6y2) = 0

Solving
23xy + 7x2 + 6y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7x + 2y)' equal to zero and attempt to solve:

Simplifying
7x + 2y = 0

Solving
7x + 2y = 0

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

Add '-2y' to each side of the equation.
7x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
7x + 0 = 0 + -2y
7x = 0 + -2y
Remove the zero:
7x = -2y

Divide each side by '7'.
x = -0.2857142857y

Simplifying
x = -0.2857142857y

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

Simplifying
x + 3y = 0

Solving
x + 3y = 0

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

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

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

Simplifying
x = -3y
Solution
x = {-0.2857142857y, -3y}

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