First, multiply each side of the equation by the common denominator of the two fractions which is #color(red)(5)color(blue)(z)#. This will eliminate the fractions while keeping the equation balanced:

#color(red)(5)color(blue)(z) xx 6/z = color(red)(5)color(blue)(z) xx 3/5#

#color(red)(5)cancel(color(blue)(z)) xx 6/color(blue)(cancel(color(black)(z))) = cancel(color(red)(5))color(blue)(z) xx 3/color(red)(cancel(color(black)(5)))#

#30 = 3z#

Now, divide each side of the equation by #color(red)(3)# to solve for #z# while keeping the equation balanced:

#30/color(red)(3) = (3z)/color(red)(3)#

#10 = (color(red)(cancel(color(red)(3)))z)/cancel(color(red)(3))#

#10 = z#

#z = 10#

Another method to solve an equation of two fractions is to "flip" the fractions and then solve for #z#:

#z/6 = 5/3#

Now multiply each side of the equation by #color(red)(6)# to solve for #z#:

#color(red)(6) xx z/6 = color(red)(6) xx 5/3#

#cancel(color(red)(6)) xx z/color(red)(cancel(color(black)(6))) = 30/3#

#z = 10#