45x^2y+300xy+500y=0

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Solution for 45x^2y+300xy+500y=0 equation: 


Simplifying
45x2y + 300xy + 500y = 0

Reorder the terms:
300xy + 45x2y + 500y = 0

Solving
300xy + 45x2y + 500y = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5y'.
5y(60x + 9x2 + 100) = 0

Factor a trinomial.
5y((3x + 10)(3x + 10)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3x + 10)' equal to zero and attempt to solve:

Simplifying
3x + 10 = 0

Reorder the terms:
10 + 3x = 0

Solving
10 + 3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x = 0 + -10
3x = 0 + -10

Combine like terms: 0 + -10 = -10
3x = -10

Divide each side by '3'.
x = -3.333333333

Simplifying
x = -3.333333333

Subproblem 3
Set the factor '(3x + 10)' equal to zero and attempt to solve:

Simplifying
3x + 10 = 0

Reorder the terms:
10 + 3x = 0

Solving
10 + 3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x = 0 + -10
3x = 0 + -10

Combine like terms: 0 + -10 = -10
3x = -10

Divide each side by '3'.
x = -3.333333333

Simplifying
x = -3.333333333
Solution
x = {-3.333333333, -3.333333333}

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