Quadratic equations - Fastest way to find the value of d

Question

$\frac{2d^2-d-10}{d^2+7d+10} = \frac{d^2-4d+3}{d^2+2d-15}$

What is the optimal solution for finding the value of d?

Answer 1

Factor the quadratics. You can pull out $x+5$ on the left and $x-3$ on the right.

Answer 2

Your expression can be written as

$$ \frac{(2d-5)(d+2)}{(d+5)(d+2)} = \frac{(d-1)(d-3)}{(d+5)(d-3)}.$$

Can you see how to proceed from here?