To solve the quadratic equation $3x^2 - 15x + 18 = 0$, follow these steps:

Step 1: Simplify by factoring out the greatest common factor (GCF)

The GCF of the coefficients $3, -15, 18$ is $3$. Factor out $3$: $3(x^2 - 5x + 6) = 0$ Divide both sides by $3$ (since $3 \neq 0$): $x^2 - 5x + 6 = 0$

Step 2: Factor the quadratic expression

Look for two numbers that multiply to $6$ (the constant term) and add to $-5$ (the coefficient of $x$): $x^2 - 5x + 6 = (x - 2)(x - 3)$

Step 3: Solve for $x$

Set each factor equal to $0$: $x - 2 = 0 \quad \text{or} \quad x - 3 = 0$ Solve for $x$: $x = 2 \quad \text{or} \quad x = 3$

Final Answer:

$x = 2, \, x = 3$

Would you like me to verify the solution or explain any step in more detail?

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Related Questions:

1. How can you verify the solutions to a quadratic equation?
2. What are the alternative methods to solve quadratic equations besides factoring?
3. What is the discriminant, and how can it confirm the number of solutions?
4. How do you handle quadratic equations that cannot be factored?
5. What are the applications of quadratic equations in real-world problems?

Tip:

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