Use the zero-product property to solve the equation \[ 5 c^{2}-11 c=12 \]

To solve the equation \( 5c^2 - 11c = 12 \), first, rearrange it to set it to zero: \[ 5c^2 - 11c - 12 = 0. \] Next, we can factor this quadratic equation. We are looking for two numbers that multiply to \( 5 \times (-12) = -60 \) and add to \( -11 \). Those numbers are \( -15 \) and \( 4 \). Now, rewrite the quadratic: \[ 5c^2 - 15c + 4c - 12 = 0. \] Next, group the terms: \[ (5c^2 - 15c) + (4c - 12) = 0, \] \[ 5c(c - 3) + 4(c - 3) = 0. \] Factor out the common term \( (c - 3) \): \[ (5c + 4)(c - 3) = 0. \] Now, apply the zero-product property: 1. Set \( 5c + 4 = 0 \) which gives \( 5c = -4 \) or \( c = -\frac{4}{5}. \) 2. Set \( c - 3 = 0 \) which gives \( c = 3. \) The solutions are: \[ c = -\frac{4}{5} \quad \text{and} \quad c = 3. \]