a=a+(n-31)d

Solution for a=a+(n-31)d equation:

Simplifying
a = a + (n + -31) * d

Reorder the terms:
a = a + (-31 + n) * d

Reorder the terms for easier multiplication:
a = a + d(-31 + n)
a = a + (-31 * d + n * d)
a = a + (-31d + dn)

Add '-1a' to each side of the equation.
a + -1a = a + -31d + -1a + dn

Combine like terms: a + -1a = 0
0 = a + -31d + -1a + dn

Reorder the terms:
0 = a + -1a + -31d + dn

Combine like terms: a + -1a = 0
0 = 0 + -31d + dn
0 = -31d + dn

Solving
0 = -31d + dn

Solving for variable 'd'.

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

Add '31d' to each side of the equation.
0 + 31d = -31d + 31d + dn
Remove the zero:
31d = -31d + 31d + dn

Combine like terms: -31d + 31d = 0
31d = 0 + dn
31d = dn

Add '-1dn' to each side of the equation.
31d + -1dn = dn + -1dn

Combine like terms: dn + -1dn = 0
31d + -1dn = 0

Factor out the Greatest Common Factor (GCF), 'd'.
d(31 + -1n) = 0

Subproblem 1
Set the factor 'd' equal to zero and attempt to solve:

Simplifying
d = 0

Solving
d = 0

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

Simplifying
d = 0
Subproblem 2
Set the factor '(31 + -1n)' equal to zero and attempt to solve:

Simplifying
31 + -1n = 0

Solving
31 + -1n = 0

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

Add '-31' to each side of the equation.
31 + -31 + -1n = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -1n = 0 + -31
-1n = 0 + -31

Combine like terms: 0 + -31 = -31
-1n = -31

Add 'n' to each side of the equation.
-1n + n = -31 + n

Combine like terms: -1n + n = 0
0 = -31 + n

Simplifying
0 = -31 + n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
d = {0}