5x^2+30xy+45y^2=0

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Solution for 5x^2+30xy+45y^2=0 equation: 


Simplifying
5x2 + 30xy + 45y2 = 0

Reorder the terms:
30xy + 5x2 + 45y2 = 0

Solving
30xy + 5x2 + 45y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6xy + x2 + 9y2) = 0

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

Ignore the factor 5.

Subproblem 1
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

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 = {-3y, -3y}

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