(12x+5y)(9y+11x)=0

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Solution for (12x+5y)(9y+11x)=0 equation: 


Simplifying
(12x + 5y)(9y + 11x) = 0

Reorder the terms:
(12x + 5y)(11x + 9y) = 0

Multiply (12x + 5y) * (11x + 9y)
(12x * (11x + 9y) + 5y * (11x + 9y)) = 0
((11x * 12x + 9y * 12x) + 5y * (11x + 9y)) = 0

Reorder the terms:
((108xy + 132x2) + 5y * (11x + 9y)) = 0
((108xy + 132x2) + 5y * (11x + 9y)) = 0
(108xy + 132x2 + (11x * 5y + 9y * 5y)) = 0
(108xy + 132x2 + (55xy + 45y2)) = 0

Reorder the terms:
(108xy + 55xy + 132x2 + 45y2) = 0

Combine like terms: 108xy + 55xy = 163xy
(163xy + 132x2 + 45y2) = 0

Solving
163xy + 132x2 + 45y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(12x + 5y)(11x + 9y) = 0


Subproblem 1
Set the factor '(12x + 5y)' equal to zero and attempt to solve:

Simplifying
12x + 5y = 0

Solving
12x + 5y = 0

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

Add '-5y' to each side of the equation.
12x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
12x + 0 = 0 + -5y
12x = 0 + -5y
Remove the zero:
12x = -5y

Divide each side by '12'.
x = -0.4166666667y

Simplifying
x = -0.4166666667y

Subproblem 2
Set the factor '(11x + 9y)' equal to zero and attempt to solve:

Simplifying
11x + 9y = 0

Solving
11x + 9y = 0

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

Add '-9y' to each side of the equation.
11x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
11x + 0 = 0 + -9y
11x = 0 + -9y
Remove the zero:
11x = -9y

Divide each side by '11'.
x = -0.8181818182y

Simplifying
x = -0.8181818182y
Solution
x = {-0.4166666667y, -0.8181818182y}

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