-2x^2 + 4x + 6 = 0 Find the roots please?

First study this page until it seems obvious: en.wikipedia.org/wiki/Polynomial_remainder_theorem

A big part of math is pattern recognition. A lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The most common pattern is (x + a) * (x + b) = x^2 + (a + b)x + ab and the special case (x + a) * (x - a) = x^2 - a^2. When you spot the pattern you can just write the answer from memory.

-2x^2 + 4x + 6 = 0 The rule is you can do any valid operation on both sides of an equation and it will still be equal. Divide by -2.

x^2 - 2x - 3 = 0 We are looking for something like (x + a)(x + b) = 0. The -3 tells that one number is negative and the only integers that qualify are 1 and 3, and the -2 tells us that the 3 is the negative number.

(x - 3)(x + 1) = 0

x = -1, 3