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The equation given is:

\[
(1 + 3x)(x - 3) = 2x^2 + 1
\]

You are asked to simplify it into its general quadratic form and find the coefficients of the quadratic, linear, and constant terms. Let's break it down step by step.

### Step 1: Expand the left-hand side
\[
(1 + 3x)(x - 3) = 1(x - 3) + 3x(x - 3)
\]
\[
= (x - 3) + 3x^2 - 9x
\]
\[
= 3x^2 - 9x + x - 3
\]
\[
= 3x^2 - 8x - 3
\]

So the left-hand side simplifies to \( 3x^2 - 8x - 3 \).

### Step 2: Set the equation in standard form
Now, rewrite the equation with both sides:
\[
3x^2 - 8x - 3 = 2x^2 + 1
\]

Move all terms to one side to form a standard quadratic equation:
\[
3x^2 - 8x - 3 - 2x^2 - 1 = 0
\]
\[
(3x^2 - 2x^2) - 8x + (-3 - 1) = 0
\]
\[
x^2 - 8x - 4 = 0
\]

### Step 3: Identify coefficients
Now the equation is in the standard form:
\[
Ax^2 + Bx + C = 0
\]
where:
- \( A = 1 \) (quadratic term coefficient),
- \( B = -8 \) (linear term coefficient),
- \( C = -4 \) (constant term).

### Final Answer:
- General form: \( x^2 - 8x - 4 = 0 \)
- Quadratic coefficient: 1
- Linear coefficient: -8
- Constant term: -4

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Do you want more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you determine if a quadratic equation has real solutions?
2. What is the discriminant of the equation \(x^2 - 8x - 4 = 0\)?
3. How can you solve a quadratic equation using the quadratic formula?
4. Can all quadratic equations be factored easily?
5. How do the signs of \(A\), \(B\), and \(C\) affect the graph of the quadratic equation?

**Tip:** To solve a quadratic equation efficiently, you can always try factoring, using the quadratic formula, or completing the square depending on the form.

Simplify the quadratic equation (1 + 3x)(x - 3) = 2x^2 + 1 into general form and find the quadratic, linear, and constant term coefficients.

Learn how to simplify and solve the quadratic equation (1 + 3x)(x - 3) = 2x^2 + 1, find the coefficients of the quadratic term, linear term, and constant term. Suitable for students in Grades 9-11.

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