To solve the equation $x(x - 3) + 2 = 0$, follow these steps:

Step 1: Expand the equation.

Distribute the $x$ over $(x - 3)$:

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

Step 2: Factor the quadratic equation.

We are now looking to factor $x^2 - 3x + 2$. Find two numbers that multiply to $2$ and add up to $-3$. These numbers are $-1$ and $-2$.

$x^2 - 3x + 2 = (x - 1)(x - 2) = 0$

Step 3: Solve for $x$.

Set each factor equal to 0:

$x - 1 = 0 \quad \text{or} \quad x - 2 = 0$

Thus, the solutions are:

$x = 1 \quad \text{or} \quad x = 2$

Final Answer:

The solutions to the equation are $x = 1$ and $x = 2$.

Would you like further details on any step?

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Here are 5 related questions to explore:

1. How do you factor a quadratic equation?
2. What is the general form of a quadratic equation?
3. Can quadratic equations have complex solutions?
4. How can you solve a quadratic equation using the quadratic formula?
5. What are the differences between factoring and completing the square?

Tip: Always check your solutions by plugging them back into the original equation.