3y^2-6x^2-3xy=0
3(y^2 - xy - 2x^2) = 0
3(y-2x)(y+x) = 0
y=2x or y = -x
The equation you have provided is a quadratic equation in terms of two variables, x and y. To solve this quadratic equation, we need to follow these steps:
Step 1: Rearrange the equation:
Start by rearranging the equation so that the terms are in order of decreasing powers. In this case, we have:
3y^2 - 3xy - 6x^2 = 0
Step 2: Factorize, if possible:
Next, try to factorize the equation. In some cases, factoring may not be possible or may be complex. However, let's see if we can factorize this particular quadratic equation.
In this case, we can factor out a common factor of 3:
3(y^2 - xy - 2x^2) = 0
Now, let's try to factor the expression in the parentheses:
(y - 2x)(y + x) = 0
So, the factored form of the equation is (y - 2x)(y + x) = 0.
Step 3: Solve for y:
To find the values of y that satisfy the equation, we set each factor equal to zero and solve for y:
Setting y - 2x = 0, we get: y = 2x
Setting y + x = 0, we get: y = -x
Therefore, the solutions to the equation 3y^2-6x^2-3xy=0 are y = 2x and y = -x.