How do i solve this problem by factoring?

Factor: Trying to factor by splitting the middle term

The first term is 15a^2, its' coefficient is 15

The middle term is - 58a, its' coefficient is - 58a

The last term is "The Constant" is +48

Multiply the coefficient of the first term by the constant 15(48) = 720

Find two factors of 720, whose sum equals the coefficient of the middle term, which is  -58

-720    +    -1    =    -721       
-360    +    -2    =    -362       
-240    +    -3    =    -243       
-180    +    -4    =    -184       
-144    +    -5    =    -149       
-120    +    -6    =    -126       
-90    +    -8    =    -98       
-80    +    -9    =    -89       
-72    +    -10    =    -82       
-60    +    -12    =    -72       
-48    +    -15    =    -63       
-45    +    -16    =    -61      
 -40    +    -18    =    -58

Factoring: 15a^2  -  58a  +  48  = 0

Factor left side of equation:
(5a - 6)(3a - 8)

Set fractions equal to Zero
5a - 6 = 0  or  3a - 8 = 0

Answer :  a = 6/5 = 1.200  
or             a = 8/3 = 2.667

Hope that helps