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

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


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

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

Reorder the terms:
1b + bx = ab + -1b + -1bx

Solving
1b + bx = ab + -1b + -1bx

Solving for variable 'b'.

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

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

Reorder the terms:
-1ab + 1b + bx = ab + -1b + -1ab + -1bx

Reorder the terms:
-1ab + 1b + bx = ab + -1ab + -1b + -1bx

Combine like terms: ab + -1ab = 0
-1ab + 1b + bx = 0 + -1b + -1bx
-1ab + 1b + bx = -1b + -1bx

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

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'b'.
b(-1a + 2 + 2x) = 0

Subproblem 1

Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0

Subproblem 2

Set the factor '(-1a + 2 + 2x)' equal to zero and attempt to solve: Simplifying -1a + 2 + 2x = 0 Reorder the terms: 2 + -1a + 2x = 0 Solving 2 + -1a + 2x = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -1a + -2 + 2x = 0 + -2 Reorder the terms: 2 + -2 + -1a + 2x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a + 2x = 0 + -2 -1a + 2x = 0 + -2 Combine like terms: 0 + -2 = -2 -1a + 2x = -2 Add 'a' to each side of the equation. -1a + a + 2x = -2 + a Combine like terms: -1a + a = 0 0 + 2x = -2 + a 2x = -2 + a Add '-2x' to each side of the equation. 2x + -2x = -2 + a + -2x Combine like terms: 2x + -2x = 0 0 = -2 + a + -2x Simplifying 0 = -2 + a + -2x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

b = {0}

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