The solutions to \( 15(2 a-2)=5\left(a^{2}-1\right) \) are:

1. Expand the left-hand side: \[ 15(2a-2)=30a-30 \] 2. Expand the right-hand side: \[ 5\left(a^{2}-1\right)=5a^2-5 \] 3. Write the equation: \[ 30a-30=5a^2-5 \] 4. Rearrange the equation to set it equal to zero: \[ 0=5a^2-5-30a+30 \] \[ 0=5a^2-30a+25 \] 5. Divide the entire equation by 5: \[ 0=a^2-6a+5 \] 6. Factor the quadratic: \[ a^2-6a+5=(a-1)(a-5)=0 \] 7. Set each factor equal to zero: \[ a-1=0 \quad \text{or} \quad a-5=0 \] 8. Solve for \(a\): \[ a=1 \quad \text{or} \quad a=5 \] The solutions are \( a=1 \) and \( a=5 \).