Simply take the inverse tangent of both sides:
#color(white)(=>)tan(4x+5)=-14#
#=>color(red)(cancel(color(black)(tan^-1)))(color(red)(cancel(color(black)tan))(4x+5))=tan^-1(-14)#
#color(white)(=>)4x+5=tan^-1(-14)#
#color(white)(=>)4x=tan^-1(-14)-5#
#color(white)(=>)x=(tan^-1(-14)-5)/4#
#color(white)(=>x)~~-1.6249...#
Now, since the period of the #tan(4x+5)# is #pi/4#, that means the answer is correct every #pi/4#, so we need to add that as a constant:
#x=(tan^-1(-14)-5)/4+(pik)/4#
where #k# is any integer.
