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

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


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

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

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

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

Combine like terms: 7xy + 6xy = 13xy
(13xy + 2x2 + 21y2) = 0

Solving
13xy + 2x2 + 21y2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

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

Simplifying
2x + 7y = 0

Solving
2x + 7y = 0

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

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

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

Divide each side by '2'.
x = -3.5y

Simplifying
x = -3.5y
Solution
x = {-3y, -3.5y}

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