Finding which base number given operations

Question

$$ (35_a + 24_a) * 21_a = 1081_a $$

Which base is the above number?

Any advice on how to solve questions like these? I tried making it in to a polynomial:

$(3a+5 + 2a+4) * (2a+1) = 108a + 1$

$10a^2 + 23a + 9 = 108a + 1$

$10a^2 - 85a + 8 =0$

But the roots of that equation do not equal the base of that number, so I obviously did something wrong

Answer 1

You've got the right idea but you need to expand $1081_a$ as $(1+8a+0a^2+1a^3)$ Then solve for $a$.