(4x+10y)(11x+5y)=0

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Solution for (4x+10y)(11x+5y)=0 equation: 


Simplifying
(4x + 10y)(11x + 5y) = 0

Multiply (4x + 10y) * (11x + 5y)
(4x * (11x + 5y) + 10y * (11x + 5y)) = 0
((11x * 4x + 5y * 4x) + 10y * (11x + 5y)) = 0

Reorder the terms:
((20xy + 44x2) + 10y * (11x + 5y)) = 0
((20xy + 44x2) + 10y * (11x + 5y)) = 0
(20xy + 44x2 + (11x * 10y + 5y * 10y)) = 0
(20xy + 44x2 + (110xy + 50y2)) = 0

Reorder the terms:
(20xy + 110xy + 44x2 + 50y2) = 0

Combine like terms: 20xy + 110xy = 130xy
(130xy + 44x2 + 50y2) = 0

Solving
130xy + 44x2 + 50y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(65xy + 22x2 + 25y2) = 0

Factor a trinomial.
2((11x + 5y)(2x + 5y)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(11x + 5y)' equal to zero and attempt to solve:

Simplifying
11x + 5y = 0

Solving
11x + 5y = 0

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

Add '-5y' to each side of the equation.
11x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
11x + 0 = 0 + -5y
11x = 0 + -5y
Remove the zero:
11x = -5y

Divide each side by '11'.
x = -0.4545454545y

Simplifying
x = -0.4545454545y

Subproblem 2
Set the factor '(2x + 5y)' equal to zero and attempt to solve:

Simplifying
2x + 5y = 0

Solving
2x + 5y = 0

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

Add '-5y' to each side of the equation.
2x + 5y + -5y = 0 + -5y

Combine like terms: 5y + -5y = 0
2x + 0 = 0 + -5y
2x = 0 + -5y
Remove the zero:
2x = -5y

Divide each side by '2'.
x = -2.5y

Simplifying
x = -2.5y
Solution
x = {-0.4545454545y, -2.5y}

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