=ax+ay+az

Solution for =ax+ay+az equation:

Simplifying
0 = ax + ay + az

Solving
0 = ax + ay + az

Solving for variable 'a'.

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

Add '-1ax' to each side of the equation.
0 + -1ax = ax + ay + -1ax + az
Remove the zero:
-1ax = ax + ay + -1ax + az

Reorder the terms:
-1ax = ax + -1ax + ay + az

Combine like terms: ax + -1ax = 0
-1ax = 0 + ay + az
-1ax = ay + az

Add '-1ay' to each side of the equation.
-1ax + -1ay = ay + -1ay + az

Combine like terms: ay + -1ay = 0
-1ax + -1ay = 0 + az
-1ax + -1ay = az

Add '-1az' to each side of the equation.
-1ax + -1ay + -1az = az + -1az

Combine like terms: az + -1az = 0
-1ax + -1ay + -1az = 0

Factor out the Greatest Common Factor (GCF), '-1a'.
-1a(x + y + z) = 0

Ignore the factor -1.
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 '(x + y + z)' equal to zero and attempt to solve:

Simplifying
x + y + z = 0

Solving
x + y + z = 0

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

Add '-1x' to each side of the equation.
x + y + -1x + z = 0 + -1x

Reorder the terms:
x + -1x + y + z = 0 + -1x

Combine like terms: x + -1x = 0
0 + y + z = 0 + -1x
y + z = 0 + -1x
Remove the zero:
y + z = -1x

Add '-1y' to each side of the equation.
y + -1y + z = -1x + -1y

Combine like terms: y + -1y = 0
0 + z = -1x + -1y
z = -1x + -1y

Add '-1z' to each side of the equation.
z + -1z = -1x + -1y + -1z

Combine like terms: z + -1z = 0
0 = -1x + -1y + -1z

Simplifying
0 = -1x + -1y + -1z

The solution to this equation could not be determined.

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