Question

Factor 6x^3 + 33^2 - 63x

Answer 1

This factors out to $3x (x + 7) (2x - 3)=0$.

First, notice that the greatest common factor of this set is $3x$.

Once you factor that out, you have a quadratic $2x^2+11x-21=0$.

You can solve this by factoring using the ac method, to find two factors whose product is -42 and whose sum is 11. These factors are 14 and -3. 

You can split the middle term b to write $2x^2+14x-3x-21=0$.

Then, you can factor to write $2x(x+7)-3(x+7)=0 \\ (2x-3)(x+7)=0$. Finally, don't forget the 3x from earlier!

This factors out to $3x (x + 7) (2x - 3)=0$.