ax+1=rt-4n

Solution for ax+1=rt-4n equation:

Simplifying
ax + 1 = rt + -4n

Reorder the terms:
1 + ax = rt + -4n

Reorder the terms:
1 + ax = -4n + rt

Solving
1 + ax = -4n + rt

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + ax = -4n + -1 + rt

Combine like terms: 1 + -1 = 0
0 + ax = -4n + -1 + rt
ax = -4n + -1 + rt

Reorder the terms:
ax = -1 + -4n + rt

Divide each side by 'x'.
a = -1x-1 + -4nx-1 + rtx-1

Simplifying
a = -1x-1 + -4nx-1 + rtx-1

Reorder the terms:
a = -4nx-1 + rtx-1 + -1x-1