How do i factor these quadratics?

6x^2-150=0

You see if they have a common factor in this case they have 6

6(x^2-25)=0

Now you see that it's a difference of two squares, meaning a square number taken away from a positive square. so you know the solution is one positive and one negative.

6(x+5)(x-5)=0

14x-3= -5x^2

You put all the x terms on one side, and see there is no common factor.

5x^2+14x-3=0

so you simply factorise by finding which number times to give you the -3 and adds to give you +14 when times by the x on the other bracket.

(5x-1)(x+3)=0