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 = 6ax
6a + 6ax = 2(3b + -2a)

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

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

Combine like terms: 6a + 4a = 10a
10a + 6ax = -4a + 4a + 6b

Combine like terms: -4a + 4a = 0
10a + 6ax = 0 + 6b
10a + 6ax = 6b

Combine like terms: 6b + -6b = 0
10a + 6ax + -6b = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5a + 3ax + -3b) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5a + 3ax + -3b)' equal to zero and attempt to solve:

Simplifying
5a + 3ax + -3b = 0

Solving
5a + 3ax + -3b = 0

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

Add '3b' to each side of the equation.
5a + 3ax + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
5a + 3ax + 0 = 0 + 3b
5a + 3ax = 0 + 3b
Remove the zero:
5a + 3ax = 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.