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

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

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

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

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

Combine like terms: ax + -1ax = 0
ab + 0 + bx = 2b(2a + x)
ab + bx = 2b(2a + x)
ab + bx = (2a * 2b + x * 2b)
ab + bx = (4ab + 2bx)

Solving
ab + bx = 4ab + 2bx

Solving for variable 'a'.

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

Add '-4ab' to each side of the equation.
ab + -4ab + bx = 4ab + -4ab + 2bx

Combine like terms: ab + -4ab = -3ab
-3ab + bx = 4ab + -4ab + 2bx

Combine like terms: 4ab + -4ab = 0
-3ab + bx = 0 + 2bx
-3ab + bx = 2bx

Add '-1bx' to each side of the equation.
-3ab + bx + -1bx = 2bx + -1bx

Combine like terms: bx + -1bx = 0
-3ab + 0 = 2bx + -1bx
-3ab = 2bx + -1bx

Combine like terms: 2bx + -1bx = 1bx
-3ab = 1bx

Divide each side by '-3b'.
a = -0.3333333333x

Simplifying
a = -0.3333333333x