Solve \( 5 t^{2}+13 t+6=0 \) by factoring. Enter your answers as a list separated by a comma \( t= \)

To solve the quadratic equation \( 5t^{2} + 13t + 6 = 0 \) by factoring, follow these steps: 1. **Multiply the coefficient of \( t^2 \) (which is 5) by the constant term (which is 6):** \[ 5 \times 6 = 30 \] 2. **Find two numbers that multiply to 30 and add up to 13:** \[ 3 \times 10 = 30 \quad \text{and} \quad 3 + 10 = 13 \] 3. **Rewrite the middle term using these two numbers:** \[ 5t^{2} + 3t + 10t + 6 = 0 \] 4. **Factor by grouping:** \[ t(5t + 3) + 2(5t + 3) = 0 \] 5. **Factor out the common term \( (5t + 3) \):** \[ (t + 2)(5t + 3) = 0 \] 6. **Set each factor equal to zero and solve for \( t \):** \[ t + 2 = 0 \quad \Rightarrow \quad t = -2 \] \[ 5t + 3 = 0 \quad \Rightarrow \quad t = -\frac{3}{5} \] **Final Answer:** \[ t= -2, -\frac{3}{5} \]