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

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

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

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

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

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

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

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

Reorder the terms:
-5a + 6ax + 1x = 2(-2a + 3b)
-5a + 6ax + 1x = (-2a * 2 + 3b * 2)
-5a + 6ax + 1x = (-4a + 6b)

Solving
-5a + 6ax + 1x = -4a + 6b

Solving for variable 'a'.

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

Add '4a' to each side of the equation.
-5a + 6ax + 4a + 1x = -4a + 4a + 6b

Reorder the terms:
-5a + 4a + 6ax + 1x = -4a + 4a + 6b

Combine like terms: -5a + 4a = -1a
-1a + 6ax + 1x = -4a + 4a + 6b

Combine like terms: -4a + 4a = 0
-1a + 6ax + 1x = 0 + 6b
-1a + 6ax + 1x = 6b

Add '-1x' to each side of the equation.
-1a + 6ax + 1x + -1x = 6b + -1x

Combine like terms: 1x + -1x = 0
-1a + 6ax + 0 = 6b + -1x
-1a + 6ax = 6b + -1x

Reorder the terms:
-1a + 6ax + -6b + x = 6b + -6b + -1x + x

Combine like terms: 6b + -6b = 0
-1a + 6ax + -6b + x = 0 + -1x + x
-1a + 6ax + -6b + x = -1x + x

Combine like terms: -1x + x = 0
-1a + 6ax + -6b + x = 0

The solution to this equation could not be determined.