The given equation appears to be:

\[
\frac{4}{3}m = \frac{-5}{3(m+3)}
\]

To solve for \( m \), follow these steps:

1. **Multiply both sides by \( 3(m+3) \) to eliminate the denominators:**

\[
(m+3)(4m) = -5
\]

2. **Distribute \( 4m \) on the left side:**

\[
4m^2 + 12m = -5
\]

3. **Move all terms to one side to form a quadratic equation:**

\[
4m^2 + 12m + 5 = 0
\]

Now, solve this quadratic equation using the quadratic formula:

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

Where \( a = 4 \), \( b = 12 \), and \( c = 5 \).

4. **Substitute the values of \( a \), \( b \), and \( c \):**

\[
m = \frac{-12 \pm \sqrt{12^2 - 4(4)(5)}}{2(4)}
\]

\[
m = \frac{-12 \pm \sqrt{144 - 80}}{8}
\]

\[
m = \frac{-12 \pm \sqrt{64}}{8}
\]

\[
m = \frac{-12 \pm 8}{8}
\]

5. **Solve for the two possible values of \( m \):**

\[
m_1 = \frac{-12 + 8}{8} = \frac{-4}{8} = -\frac{1}{2}
\]
\[
m_2 = \frac{-12 - 8}{8} = \frac{-20}{8} = -\frac{5}{2}
\]

Therefore, the solutions for \( m \) are:

\[
m = -\frac{1}{2} \quad \text{or} \quad m = -\frac{5}{2}
\]

---

Would you like a detailed explanation of any steps?

Here are 5 related questions to consider:
1. How do you solve general quadratic equations?
2. What is the discriminant, and how does it affect the number of solutions in a quadratic equation?
3. Can all quadratic equations be solved using the quadratic formula?
4. How can we factor a quadratic equation to solve it?
5. What are the properties of the solutions to quadratic equations in different contexts?

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

Solve for m.
4
3
m = –
m + 5
3
m + 3
m =

Learn how to solve a quadratic equation involving rational expressions. This step-by-step guide shows how to solve for m using the quadratic formula after simplifying the given equation. Suitable for students in Grades 9-11.

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