9x^2+10xy+y^2=0

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Solution for 9x^2+10xy+y^2=0 equation: 


Simplifying
9x2 + 10xy + y2 = 0

Reorder the terms:
10xy + 9x2 + y2 = 0

Solving
10xy + 9x2 + y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(9x + y)' equal to zero and attempt to solve:

Simplifying
9x + y = 0

Solving
9x + y = 0

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

Add '-1y' to each side of the equation.
9x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
9x + 0 = 0 + -1y
9x = 0 + -1y
Remove the zero:
9x = -1y

Divide each side by '9'.
x = -0.1111111111y

Simplifying
x = -0.1111111111y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {-0.1111111111y, -1y}

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