The given equation is:

$6 - 3x^2 = 3$

We will solve this step by step.

Step 1: Simplify the equation

First, subtract 3 from both sides of the equation:

$6 - 3x^2 - 3 = 0$

This simplifies to:

$3 - 3x^2 = 0$

Step 2: Isolate the $x^2$ term

Now, subtract 3 from both sides:

$-3x^2 = -3$

Step 3: Solve for $x^2$

Divide both sides by $-3$:

$x^2 = 1$

Step 4: Solve for $x$

Take the square root of both sides:

$x = \pm 1$

Thus, the solution is:

$x = 1 \quad \text{or} \quad x = -1$

Would you like more details or have any questions about this solution?

Here are 5 related questions to extend your understanding:

1. How do you verify if both solutions $x = 1$ and $x = -1$ satisfy the original equation?
2. What is the general form of a quadratic equation?
3. How does the discriminant of a quadratic equation help determine the number of solutions?
4. Could this equation have been solved by factoring? Why or why not?
5. What are some methods to solve quadratic equations other than taking square roots?

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