Multiply. Write your answer in simplest form. \( \frac{10 d+2}{d^{2}-d} \cdot \frac{3 d^{2}+5 d}{2} \)

Calculate or simplify the expression \( (10d+2)/(d^2-d) * (3d^2+5d)/2 \). Simplify the expression by following steps: - step0: Solution: \(\frac{\frac{\left(10d+2\right)}{\left(d^{2}-d\right)}\times \left(3d^{2}+5d\right)}{2}\) - step1: Remove the parentheses: \(\frac{\frac{10d+2}{d^{2}-d}\times \left(3d^{2}+5d\right)}{2}\) - step2: Multiply the terms: \(\frac{\frac{\left(10d+2\right)\left(3d+5\right)}{d-1}}{2}\) - step3: Multiply by the reciprocal: \(\frac{\left(10d+2\right)\left(3d+5\right)}{d-1}\times \frac{1}{2}\) - step4: Rewrite the expression: \(\frac{2\left(5d+1\right)\left(3d+5\right)}{d-1}\times \frac{1}{2}\) - step5: Reduce the fraction: \(\frac{\left(5d+1\right)\left(3d+5\right)}{d-1}\times 1\) - step6: Multiply the terms: \(\frac{\left(5d+1\right)\left(3d+5\right)}{d-1}\) - step7: Multiply the terms: \(\frac{15d^{2}+28d+5}{d-1}\) The product of \( \frac{10d+2}{d^{2}-d} \) and \( \frac{3d^{2}+5d}{2} \) is \( \frac{15d^{2}+28d+5}{d-1} \).