(x+1)(1+a)=2ax-a(x-3)

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

Simplifying
(x + 1)(1 + a) = 2ax + -1a(x + -3)

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

Multiply (1 + x) * (1 + a)
(1(1 + a) + x(1 + a)) = 2ax + -1a(x + -3)
((1 * 1 + a * 1) + x(1 + a)) = 2ax + -1a(x + -3)
((1 + 1a) + x(1 + a)) = 2ax + -1a(x + -3)
(1 + 1a + (1 * x + a * x)) = 2ax + -1a(x + -3)

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

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

Reorder the terms:
1 + 1a + ax + 1x = 3a + 2ax + -1ax

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

Solving
1 + 1a + ax + 1x = 3a + 1ax

Solving for variable 'a'.

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

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

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

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

Combine like terms: 3a + -3a = 0
1 + -2a + ax + 1x = 0 + 1ax
1 + -2a + ax + 1x = 1ax

Add '-1ax' to each side of the equation.
1 + -2a + ax + -1ax + 1x = 1ax + -1ax

Combine like terms: ax + -1ax = 0
1 + -2a + 0 + 1x = 1ax + -1ax
1 + -2a + 1x = 1ax + -1ax

Combine like terms: 1ax + -1ax = 0
1 + -2a + 1x = 0

Add '-1' to each side of the equation.
1 + -2a + -1 + 1x = 0 + -1

Reorder the terms:
1 + -1 + -2a + 1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a + 1x = 0 + -1
-2a + 1x = 0 + -1

Combine like terms: 0 + -1 = -1
-2a + 1x = -1

Add '-1x' to each side of the equation.
-2a + 1x + -1x = -1 + -1x

Combine like terms: 1x + -1x = 0
-2a + 0 = -1 + -1x
-2a = -1 + -1x

Divide each side by '-2'.
a = 0.5 + 0.5x

Simplifying
a = 0.5 + 0.5x