To factor quadratics in the form #ax^2+bx+c#, we need to find two numbers that multiply to #a*c# and add up to #b#.
In our case, we need to find the two numbers that multiply to #60# and add up to #17#.
After some experimentation, you will find that these two numbers are #5# and #12#. Now, split up the #x# terms into #5# and #12#, then factor by grouping. It will look like this:
#15x^2+17x+4=0#
#15x^2+5x+12x+4=0#
#color(red)(5x)*3x+color(red)(5x)*1+12x+4=0#
#color(red)(5x)(3x+1)+12x+4=0#
#color(red)(5x)(3x+1)+color(blue)4*3x+color(blue)4*1=0#
#color(red)(5x)(3x+1)+color(blue)4(3x+1)=0#
#(color(red)(5x)+color(blue)4)(3x+1)=0#
Now, to solve for #x#, set each of these factors equal to #0# to find out what the #x# value will be:
#color(white){color(black)(
(5x+4=0,qquadqquad3x+1=0),
(5x=-4,qquadqquad3x=-1),
(x=-4/5,qquadqquadx=-1/3):}#
These are the solutions. Hope this is the answer you were looking for!
