The equation \( 3-2y^2 = y^2 \) can be solved by following these steps:

1. Simplify the equation:
   \[
   3 - 2y^2 = y^2
   \]

2. Combine like terms:
   \[
   3 - 2y^2 - y^2 = 0
   \]

3. Simplify further:
   \[
   3 - 3y^2 = 0
   \]

4. Add \( 3y^2 \) to both sides:
   \[
   3 = 3y^2
   \]

5. Divide both sides by 3:
   \[
   1 = y^2
   \]

6. Take the square root of both sides:
   \[
   y = \pm 1
   \]

Therefore, the solutions to the equation are \( y = 1 \) and \( y = -1 \).

Would you like more details or have any questions?

Here are some related questions:

1. What are the steps to solve quadratic equations in general?
2. How do you combine like terms in an equation?
3. What does it mean to take the square root of both sides of an equation?
4. Are there other methods to solve \( y^2 = 1 \)?
5. How do you check if your solutions to a quadratic equation are correct?
6. Can quadratic equations have complex solutions?
7. How do you solve quadratic equations using the quadratic formula?
8. What are the properties of the solutions to \( y^2 = k \) for any real number \( k \)?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy the equation.

Learn how to solve the equation 3 - 2y^2 = y^2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including quadratic equations and their solutions. Suitable for advanced high school students (Grades 10-12).

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