(x+6y)(7x+3y)=

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Solution for (x+6y)(7x+3y)= equation: 


Simplifying
(x + 6y)(7x + 3y) = 0

Multiply (x + 6y) * (7x + 3y)
(x(7x + 3y) + 6y * (7x + 3y)) = 0
((7x * x + 3y * x) + 6y * (7x + 3y)) = 0

Reorder the terms:
((3xy + 7x2) + 6y * (7x + 3y)) = 0
((3xy + 7x2) + 6y * (7x + 3y)) = 0
(3xy + 7x2 + (7x * 6y + 3y * 6y)) = 0
(3xy + 7x2 + (42xy + 18y2)) = 0

Reorder the terms:
(3xy + 42xy + 7x2 + 18y2) = 0

Combine like terms: 3xy + 42xy = 45xy
(45xy + 7x2 + 18y2) = 0

Solving
45xy + 7x2 + 18y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + 3y)(x + 6y) = 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 + 6y)' equal to zero and attempt to solve:

Simplifying
x + 6y = 0

Solving
x + 6y = 0

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

Add '-6y' to each side of the equation.
x + 6y + -6y = 0 + -6y

Combine like terms: 6y + -6y = 0
x + 0 = 0 + -6y
x = 0 + -6y
Remove the zero:
x = -6y

Simplifying
x = -6y
Solution
x = {-0.4285714286y, -6y}

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