((9x+6y)(10x+30y))=

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Solution for ((9x+6y)(10x+30y))= equation: 


Simplifying
((9x + 6y)(10x + 30y)) = 0

Multiply (9x + 6y) * (10x + 30y)
((9x * (10x + 30y) + 6y * (10x + 30y))) = 0
(((10x * 9x + 30y * 9x) + 6y * (10x + 30y))) = 0

Reorder the terms:
(((270xy + 90x2) + 6y * (10x + 30y))) = 0
(((270xy + 90x2) + 6y * (10x + 30y))) = 0
((270xy + 90x2 + (10x * 6y + 30y * 6y))) = 0
((270xy + 90x2 + (60xy + 180y2))) = 0

Reorder the terms:
((270xy + 60xy + 90x2 + 180y2)) = 0

Combine like terms: 270xy + 60xy = 330xy
((330xy + 90x2 + 180y2)) = 0
(330xy + 90x2 + 180y2) = 0

Remove parenthesis around (330xy + 90x2 + 180y2)
330xy + 90x2 + 180y2 = 0

Solving
330xy + 90x2 + 180y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '30'.
30(11xy + 3x2 + 6y2) = 0

Factor a trinomial.
30((3x + 2y)(x + 3y)) = 0

Ignore the factor 30.

Subproblem 1
Set the factor '(3x + 2y)' equal to zero and attempt to solve:

Simplifying
3x + 2y = 0

Solving
3x + 2y = 0

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

Add '-2y' to each side of the equation.
3x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
3x + 0 = 0 + -2y
3x = 0 + -2y
Remove the zero:
3x = -2y

Divide each side by '3'.
x = -0.6666666667y

Simplifying
x = -0.6666666667y

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 = {-0.6666666667y, -3y}

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