45x^2+38xy+8y^2=0

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Solution for 45x^2+38xy+8y^2=0 equation: 


Simplifying
45x2 + 38xy + 8y2 = 0

Reorder the terms:
38xy + 45x2 + 8y2 = 0

Solving
38xy + 45x2 + 8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5x + 2y)(9x + 4y) = 0


Subproblem 1
Set the factor '(5x + 2y)' equal to zero and attempt to solve:

Simplifying
5x + 2y = 0

Solving
5x + 2y = 0

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

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

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

Divide each side by '5'.
x = -0.4y

Simplifying
x = -0.4y

Subproblem 2
Set the factor '(9x + 4y)' equal to zero and attempt to solve:

Simplifying
9x + 4y = 0

Solving
9x + 4y = 0

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

Add '-4y' to each side of the equation.
9x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
9x + 0 = 0 + -4y
9x = 0 + -4y
Remove the zero:
9x = -4y

Divide each side by '9'.
x = -0.4444444444y

Simplifying
x = -0.4444444444y
Solution
x = {-0.4y, -0.4444444444y}

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