you need to factor it using the AC method.
then we need to find two numbers the multiply and give us 30 and add to 13. those numbers are 10 and 3. so now we split the 13x up to be 10x+3x then factor by grouping
5x^2+10x+3x+6=0 group the 1st 2 and the 2nd 2
(5x^2+10x)+(3x+6)=0 then factor out the common factor of each group
5x(x+2)+3(x+2)=0 then factor out the parentheses as a common factor
(x+2)(5x+3)=0 then set each parenthesis equal to 0 and then solve