6-2x-1=rx+5-6x

Solution for 6-2x-1=rx+5-6x equation:

Simplifying
6 + -2x + -1 = rx + 5 + -6x

Reorder the terms:
6 + -1 + -2x = rx + 5 + -6x

Combine like terms: 6 + -1 = 5
5 + -2x = rx + 5 + -6x

Reorder the terms:
5 + -2x = 5 + rx + -6x

Add '-5' to each side of the equation.
5 + -5 + -2x = 5 + rx + -5 + -6x

Combine like terms: 5 + -5 = 0
0 + -2x = 5 + rx + -5 + -6x
-2x = 5 + rx + -5 + -6x

Reorder the terms:
-2x = 5 + -5 + rx + -6x

Combine like terms: 5 + -5 = 0
-2x = 0 + rx + -6x
-2x = rx + -6x

Solving
-2x = rx + -6x

Solving for variable 'x'.

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

Add '-1rx' to each side of the equation.
-1rx + -2x = rx + -1rx + -6x

Combine like terms: rx + -1rx = 0
-1rx + -2x = 0 + -6x
-1rx + -2x = -6x

Add '6x' to each side of the equation.
-1rx + -2x + 6x = -6x + 6x

Combine like terms: -2x + 6x = 4x
-1rx + 4x = -6x + 6x

Combine like terms: -6x + 6x = 0
-1rx + 4x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1r + 4) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-1r + 4)' equal to zero and attempt to solve:

Simplifying
-1r + 4 = 0

Reorder the terms:
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Add 'r' to each side of the equation.
-1r + r = -4 + r

Combine like terms: -1r + r = 0
0 = -4 + r

Simplifying
0 = -4 + r

The solution to this equation could not be determined.

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