4x^2+20xy+9y^2=0

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Solution for 4x^2+20xy+9y^2=0 equation: 


Simplifying
4x2 + 20xy + 9y2 = 0

Reorder the terms:
20xy + 4x2 + 9y2 = 0

Solving
20xy + 4x2 + 9y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2x + y)(2x + 9y) = 0


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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y

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

Simplifying
2x + 9y = 0

Solving
2x + 9y = 0

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

Add '-9y' to each side of the equation.
2x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
2x + 0 = 0 + -9y
2x = 0 + -9y
Remove the zero:
2x = -9y

Divide each side by '2'.
x = -4.5y

Simplifying
x = -4.5y
Solution
x = {-0.5y, -4.5y}

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