(x+r)t+1=0

Solution for (x+r)t+1=0 equation:

Simplifying
(x + r) * t + 1 = 0

Reorder the terms:
(r + x) * t + 1 = 0

Reorder the terms for easier multiplication:
t(r + x) + 1 = 0
(r * t + x * t) + 1 = 0
(rt + tx) + 1 = 0

Reorder the terms:
1 + rt + tx = 0

Solving
1 + rt + tx = 0

Solving for variable 'r'.

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

Add '-1' to each side of the equation.
1 + rt + -1 + tx = 0 + -1

Reorder the terms:
1 + -1 + rt + tx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + rt + tx = 0 + -1
rt + tx = 0 + -1

Combine like terms: 0 + -1 = -1
rt + tx = -1

Add '-1tx' to each side of the equation.
rt + tx + -1tx = -1 + -1tx

Combine like terms: tx + -1tx = 0
rt + 0 = -1 + -1tx
rt = -1 + -1tx

Divide each side by 't'.
r = -1t-1 + -1x

Simplifying
r = -1t-1 + -1x