How do I solve for d

I have a physics problem which I mostly solved, however I'm having a bit of trouble with the algebra in it. Everything is symbols so I can't speed things up by much here. I've spent quite a while trying to figure it out but (L-d) is constantly messing up my equations.

Here is the formula:

(d)(L^2)(p2)(g) + (L-d)(L^2)(p3)(g) = (p1)(L^3)(g)

and I need a formula that has d = ...

I could be way over thinking this but I don't believe I am, so any help would be appreciated.

Please note that p1, p2, and p3 are all different variables.

from the left you can pull out g and L^2 so you have

(g*L^2)(d*p2+(L-d)*p3)=p1(L^3)g

then divide the (g*L^2) from both sides.

d*p2+(L-d)*p3 = p1*L

then multiply the p3 in which gives

d*p2+L*p3-d*p3 = p1*L

then subtract L*p3 from both sides

d*p2-d*p3 = p1*L-L*p3

then pull the d out from the right.

d(p2-p3) = p1*L-L*p3

then divide both sides by (p2-p3) which leaves you with

d=(p1*L-L*p3)/(p2-p3).

then you can simplify by pulling the L out of the top.

d=(L(p1-p3))/(p2-p3)

(d)(L^2)(p2)(g) + (L - d)(L^2)(p3)(g) = (p1)(L^3)(g)

Factor

(L^2)(g)((d)(p2) + (L - d)(p3)) = (p1)(L^3)(g)
(d)(p2) + (L - d)(p3) = (p1)(L^3)(g) / (L^2)(g)
(d)(p2) + (L - d)(p3) = (p1)(L)

Distribute

(d)(p2) + (L)(p3) - (d)(p3) = (p1)(L)

Factor

d(p2 - p3) + (L)(p3) = (p1)(L)

Bring over the (L)(p3)

d(p2 - p3) = (p1)(L) - (L)(p3)
d(p2 - p3) = L(p1 - p3)

Divide

d = L(p1 - p3) / (p2 - p3)

(d)(L^2)(p2)(g) + (L- d)(L^2)(p3)(g) = (p1)(L^3)(g)
(d)(L^2)(p2)(g) + (L)(L^2)(p3)(g) - (d)(L^2)(p3)(g) = (p1)(L^3)(g)
(d)(g)(L^2)(p2 - p3) = (g)((p1)(L^3) - (L)(L^2)(p3))
(d) = [(g)((p1)(L^3) - (L)(L^2)(p3))] / (g)(L^2)(p2 - p3)
(d) = [(p1)(L^3) - (L)(L^2)(p3)] / (L^2)(p2 - p3)
(d) = [(p1)(L^3) - (L^3)(p3)] / (L^2)(p2 - p3)
(d) = [(L^3)((p1) - (p3))] / (L^2)(p2 - p3)
(d) = [(L)((p1) - (p3))] / (p2 - p3)