Try this lesson on factoring quadratics.
(The posted link was for solving equations, rather than factoring expressions.)
I've been doing this by trial and error but it takes too long. I tried googling "factoring quadratics" but when it comes to examples like this, they just use the quadratic equation to find the values of x assuming the whole equation was equal to zero in the first place. I don't think this helps me.
I need the answer in the form (....)(....) and I don't think the answer on, for example, Solving Quadratic Equations: Examples, does that. What I need is the strategy to find this. I know I'm going to need +7. -5 or -7, +5 at the ends but from there I just have to try so many combinations.
Here's one strategy you might find helpful.
Multiply the leading coefficient (6) by your constant (-35) to get -210.
Next, try to come up with 2 factors that multiply to get -210 and sum to +11.
You may have to fiddle around a little to find them, but this one came to me right away. It's +21 and -10.
Replace the middle coefficient (-11) with these two numbers:
Now, group the first two terms and the last 2 terms and factor out the greatest common factor for each.
Use the distributive property to finish up.