Solving the Equation: 2x + 3y^2 + 3x^2y = 4x^2
In this article, we will solve the equation 2x + 3y^2 + 3x^2y = 4x^2. This equation involves variables x and y, and our goal is to find the values of x and y that satisfy the equation.
Step 1: Simplify the Equation
First, let's simplify the equation by combining like terms:
2x + 3y^2 + 3x^2y = 4x^2
Step 2: Move All Terms to One Side
Next, let's move all terms to the left-hand side of the equation:
2x - 4x^2 + 3y^2 + 3x^2y = 0
Step 3: Factor Out x
Notice that x is a common factor in two of the terms. Let's factor out x:
x(2 - 4x + 3xy) + 3y^2 = 0
Step 4: Solve for x
Now, let's solve for x. We can do this by setting each factor equal to 0 and solving for x:
x = 0 or 2 - 4x + 3xy = 0
The first solution, x = 0, is trivial. Let's focus on the second solution:
2 - 4x + 3xy = 0
Step 5: Solve for y
Now, let's solve for y. We can do this by rearranging the equation to isolate y:
3xy = 4x - 2
y = (4x - 2) / (3x)
Step 6: Write the Solution
The final solution is:
x = 0 or x = (4x - 2) / (3x)
y = (4x - 2) / (3x)
This is the solution to the equation 2x + 3y^2 + 3x^2y = 4x^2. Note that the solution involves both x and y, and we can plug in different values of x to find the corresponding values of y.
