Solve by applying the zero product property. \[ 15 m(m+3)=14 m-10 \] If there is more than one solution, separate the answers with commas.

To solve the equation \( 15m(m + 3) = 14m - 10 \) using the zero product property, follow these steps: 1. **Expand and Rearrange the Equation:** First, move all terms to one side of the equation to set it to zero. \[ 15m(m + 3) - 14m + 10 = 0 \] Expand the left side: \[ 15m^2 + 45m - 14m + 10 = 0 \] Combine like terms: \[ 15m^2 + 31m + 10 = 0 \] 2. **Factor the Quadratic Equation:** To factor \( 15m^2 + 31m + 10 \), look for two numbers that multiply to \( 15 \times 10 = 150 \) and add up to \( 31 \). These numbers are \( 6 \) and \( 25 \). Rewrite the middle term using these numbers: \[ 15m^2 + 6m + 25m + 10 = 0 \] Factor by grouping: \[ 3m(5m + 2) + 5(5m + 2) = 0 \] Factor out the common term \( (5m + 2) \): \[ (3m + 5)(5m + 2) = 0 \] 3. **Apply the Zero Product Property:** Set each factor equal to zero: \[ 3m + 5 = 0 \quad \text{or} \quad 5m + 2 = 0 \] Solve for \( m \): \[ m = -\frac{5}{3} \quad \text{or} \quad m = -\frac{2}{5} \] **Solutions:** \[ m = -\frac{5}{3},\ -\frac{2}{5} \]