ar+as-at=

Solution for ar+as-at= equation:

Simplifying
ar + as + -1at = 0

Solving
ar + as + -1at = 0

Solving for variable 'a'.

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

Factor out the Greatest Common Factor (GCF), 'a'.
a(r + s + -1t) = 0

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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(r + s + -1t)' equal to zero and attempt to solve:

Simplifying
r + s + -1t = 0

Solving
r + s + -1t = 0

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

Add '-1r' to each side of the equation.
r + s + -1r + -1t = 0 + -1r

Reorder the terms:
r + -1r + s + -1t = 0 + -1r

Combine like terms: r + -1r = 0
0 + s + -1t = 0 + -1r
s + -1t = 0 + -1r
Remove the zero:
s + -1t = -1r

Add '-1s' to each side of the equation.
s + -1s + -1t = -1r + -1s

Combine like terms: s + -1s = 0
0 + -1t = -1r + -1s
-1t = -1r + -1s

Add 't' to each side of the equation.
-1t + t = -1r + -1s + t

Combine like terms: -1t + t = 0
0 = -1r + -1s + t

Simplifying
0 = -1r + -1s + t

The solution to this equation could not be determined.

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