Start with
[tex]D=\dfrac{15u}{3u+6}-1[/tex]
add 1 to both sides:
[tex]D+1=\dfrac{15u}{3u+6}[/tex]
Multiply both sides by 3u+6:
[tex](3u+6)(D+1)=15u[/tex]
Expand the left hand side:
[tex]3Du+3u+6D+6=15u[/tex]
Move all terms involving u to the left, and all terms not involving u to the right.
[tex]3Du+3u-15u=-6D-6[/tex]
Sum like terms:
[tex]3Du-12u=-6D-6[/tex]
Factor u:
[tex]u(3D-12)=-6D-6[/tex]
Divide both sides by 3D-12:
[tex]u=-\dfrac{6D+6}{3D-12}[/tex]
