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

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

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

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

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

Reorder the terms:
2a + 2ax = (ax + a2) + 5a
2a + 2ax = (ax + a2) + 5a

Reorder the terms:
2a + 2ax = 5a + ax + a2

Solving
2a + 2ax = 5a + ax + a2

Solving for variable 'a'.

Reorder the terms:
2a + -5a + 2ax + -1ax + -1a2 = 5a + ax + a2 + -5a + -1ax + -1a2

Combine like terms: 2a + -5a = -3a
-3a + 2ax + -1ax + -1a2 = 5a + ax + a2 + -5a + -1ax + -1a2

Combine like terms: 2ax + -1ax = 1ax
-3a + 1ax + -1a2 = 5a + ax + a2 + -5a + -1ax + -1a2

Reorder the terms:
-3a + 1ax + -1a2 = 5a + -5a + ax + -1ax + a2 + -1a2

Combine like terms: 5a + -5a = 0
-3a + 1ax + -1a2 = 0 + ax + -1ax + a2 + -1a2
-3a + 1ax + -1a2 = ax + -1ax + a2 + -1a2

Combine like terms: ax + -1ax = 0
-3a + 1ax + -1a2 = 0 + a2 + -1a2
-3a + 1ax + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-3a + 1ax + -1a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-3 + x + -1a) = 0

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 '(-3 + x + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + x + -1a = 0

Reorder the terms:
-3 + -1a + x = 0

Solving
-3 + -1a + x = 0

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

Add '3' to each side of the equation.
-3 + -1a + 3 + x = 0 + 3

Reorder the terms:
-3 + 3 + -1a + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a + x = 0 + 3
-1a + x = 0 + 3

Combine like terms: 0 + 3 = 3
-1a + x = 3

Add '-1x' to each side of the equation.
-1a + x + -1x = 3 + -1x

Combine like terms: x + -1x = 0
-1a + 0 = 3 + -1x
-1a = 3 + -1x

Divide each side by '-1'.
a = -3 + x

Simplifying
a = -3 + x
Solution
a = {0, -3 + x}