a(x+1)+5a(x-1)=2(3a-2a)

Solution for a(x+1)+5a(x-1)=2(3a-2a) equation:

Simplifying
a(x + 1) + 5a(x + -1) = 2(3a + -2a)

Reorder the terms:
a(1 + x) + 5a(x + -1) = 2(3a + -2a)
(1 * a + x * a) + 5a(x + -1) = 2(3a + -2a)
(1a + ax) + 5a(x + -1) = 2(3a + -2a)

Reorder the terms:
1a + ax + 5a(-1 + x) = 2(3a + -2a)
1a + ax + (-1 * 5a + x * 5a) = 2(3a + -2a)
1a + ax + (-5a + 5ax) = 2(3a + -2a)

Reorder the terms:
1a + -5a + ax + 5ax = 2(3a + -2a)

Combine like terms: 1a + -5a = -4a
-4a + ax + 5ax = 2(3a + -2a)

Combine like terms: ax + 5ax = 6ax
-4a + 6ax = 2(3a + -2a)

Combine like terms: 3a + -2a = 1a
-4a + 6ax = 2(1a)

Remove parenthesis around (1a)
-4a + 6ax = 2 * 1a

Multiply 2 * 1
-4a + 6ax = 2a

Solving
-4a + 6ax = 2a

Solving for variable 'a'.

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

Add '-2a' to each side of the equation.
-4a + -2a + 6ax = 2a + -2a

Combine like terms: -4a + -2a = -6a
-6a + 6ax = 2a + -2a

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

Factor out the Greatest Common Factor (GCF), '6a'.
6a(-1 + x) = 0

Ignore the factor 6.
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 '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

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

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

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

Combine like terms: 0 + 1 = 1
x = 1

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

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

Simplifying
0 = 1 + -1x

The solution to this equation could not be determined.

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