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

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

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

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

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

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

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

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

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

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

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

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

Solving
6ax = 4b

Solving for variable 'a'.

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

Divide each side by '6x'.
a = 0.6666666667bx-1

Simplifying
a = 0.6666666667bx-1