2-6x=2(ax+1)

Solution for 2-6x=2(ax+1) equation:

Simplifying
2 + -6x = 2(ax + 1)

Reorder the terms:
2 + -6x = 2(1 + ax)
2 + -6x = (1 * 2 + ax * 2)
2 + -6x = (2 + 2ax)

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

Combine like terms: 2 + -2 = 0
0 + -6x = 2 + -2 + 2ax
-6x = 2 + -2 + 2ax

Combine like terms: 2 + -2 = 0
-6x = 0 + 2ax
-6x = 2ax

Solving
-6x = 2ax

Solving for variable 'x'.

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

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

Combine like terms: 2ax + -2ax = 0
-2ax + -6x = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(a + 3) = 0

Ignore the factor -2.
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 '(a + 3)' equal to zero and attempt to solve:

Simplifying
a + 3 = 0

Reorder the terms:
3 + a = 0

Solving
3 + a = 0

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

Add '-3' to each side of the equation.
3 + -3 + a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + a = 0 + -3
a = 0 + -3

Combine like terms: 0 + -3 = -3
a = -3

Add '-1a' to each side of the equation.
a + -1a = -3 + -1a

Combine like terms: a + -1a = 0
0 = -3 + -1a

Simplifying
0 = -3 + -1a

The solution to this equation could not be determined.

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