6x*x+11*xy+5y*y=0

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Solution for 6x*x+11*xy+5y*y=0 equation:


Simplifying
6x * x + 11xy + 5y * y = 0

Multiply x * x
6x2 + 11xy + 5y * y = 0

Multiply y * y
6x2 + 11xy + 5y2 = 0

Reorder the terms:
11xy + 6x2 + 5y2 = 0

Solving
11xy + 6x2 + 5y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6x + 5y)(x + y) = 0

Subproblem 1

Set the factor '(6x + 5y)' equal to zero and attempt to solve: Simplifying 6x + 5y = 0 Solving 6x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 6x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 6x + 0 = 0 + -5y 6x = 0 + -5y Remove the zero: 6x = -5y Divide each side by '6'. x = -0.8333333333y Simplifying x = -0.8333333333y

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 = {-0.8333333333y, -1y}

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