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

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

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

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

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

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

Combine like terms: 1a + 5a = 6a
6a + ax + -5ax = 2(3b + -2A)

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

Reorder the terms:
6a + -4ax = 2(-2A + 3b)
6a + -4ax = (-2A * 2 + 3b * 2)
6a + -4ax = (-4A + 6b)

Solving
6a + -4ax = -4A + 6b

Solving for variable 'a'.

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

Reorder the terms:
4A + 6a + -4ax + -6b = -4A + 6b + 4A + -6b

Reorder the terms:
4A + 6a + -4ax + -6b = -4A + 4A + 6b + -6b

Combine like terms: -4A + 4A = 0
4A + 6a + -4ax + -6b = 0 + 6b + -6b
4A + 6a + -4ax + -6b = 6b + -6b

Combine like terms: 6b + -6b = 0
4A + 6a + -4ax + -6b = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(2A + 3a + -2ax + -3b)' equal to zero and attempt to solve:

Simplifying
2A + 3a + -2ax + -3b = 0

Solving
2A + 3a + -2ax + -3b = 0

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

Add '-2A' to each side of the equation.
2A + 3a + -2ax + -2A + -3b = 0 + -2A

Reorder the terms:
2A + -2A + 3a + -2ax + -3b = 0 + -2A

Combine like terms: 2A + -2A = 0
0 + 3a + -2ax + -3b = 0 + -2A
3a + -2ax + -3b = 0 + -2A
Remove the zero:
3a + -2ax + -3b = -2A

Add '3b' to each side of the equation.
3a + -2ax + -3b + 3b = -2A + 3b

Combine like terms: -3b + 3b = 0
3a + -2ax + 0 = -2A + 3b
3a + -2ax = -2A + 3b

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.