First, multiply each side of the equation by #color(red)((2 - 7x^4))# to isolate the #z# term while keeping the equation balanced:

#15 xx color(red)((2 - 7x^4)) = (10z)/(2 - 7x^4) xx color(red)((2 - 7x^4))#

#15color(red)((2 - 7x^4)) = (10z)/color(red)(cancel(color(black)(2 - 7x^4))) xx cancel(color(red)((2 - 7x^4)))#

#15(2 - 7x^4) = 10z#

Now, divide each side of the equation by #color(red)(10)# to solve for #z# while keeping the equation balanced:

#(15(2 - 7x^4))/color(red)(10) = (10z)/color(red)(10)#

#((5 xx 3)(2 - 7x^4))/color(red)(5 xx 2) = (color(red)(cancel(color(black)(10)))z)/cancel(color(red)(10))#

#((color(red)(cancel(color(black)(5))) xx 3)(2 - 7x^4))/color(red)(color(black)(cancel(color(red)(5))) xx 2) = z#

#(3(2 - 7x^4))/2 = z#

#z = (3(2 - 7x^4))/2#

Or

#z = ((3 xx 2) - (3 xx 7x^4))/2#

#z = (6 - 21x^4)/2#

Or

#z = 6/2 - (21x^4)/2#

#z = 3 - (21x^4)/2#