Let's simplify and solve the quadratic equation:

\[
12x^2 - 18x - 2x + 3 = 0
\]

### Step 1: Combine like terms.
Combine the terms involving \(x\):

\[
12x^2 - (18x + 2x) + 3 = 0
\]

\[
12x^2 - 20x + 3 = 0
\]

### Step 2: Use the quadratic formula.
For a quadratic equation of the form \(ax^2 + bx + c = 0\), the quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Here, \(a = 12\), \(b = -20\), and \(c = 3\).

### Step 3: Plug values into the quadratic formula.
\[
x = \frac{-(-20) \pm \sqrt{(-20)^2 - 4(12)(3)}}{2(12)}
\]

\[
x = \frac{20 \pm \sqrt{400 - 144}}{24}
\]

\[
x = \frac{20 \pm \sqrt{256}}{24}
\]

\[
x = \frac{20 \pm 16}{24}
\]

### Step 4: Solve for \(x\).
1. \(x = \frac{20 + 16}{24} = \frac{36}{24} = \frac{3}{2}\)
2. \(x = \frac{20 - 16}{24} = \frac{4}{24} = \frac{1}{6}\)

### Final solutions:
\[
x = \frac{3}{2} \quad \text{or} \quad x = \frac{1}{6}
\]

Would you like more details on any step?

Here are 5 related questions:
1. What are the steps to solve quadratic equations using factoring?
2. Can every quadratic equation be solved using the quadratic formula?
3. How do you determine if a quadratic equation has real or complex solutions?
4. What is the discriminant, and what does it tell us about a quadratic equation?
5. Can you solve quadratic equations by completing the square?

**Tip**: Always check the discriminant (\(b^2 - 4ac\)) before solving to determine the nature of the roots (real or complex).

Learn how to solve the quadratic equation 12x² - 18x - 2x + 3 = 0 using the quadratic formula. This step-by-step solution simplifies the equation by combining like terms and applying the quadratic formula. Suitable for students in Grades 9-11.

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