ax+b+ab=b

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Solution for ax+b+ab=b equation:


Simplifying
ax + b + ab = b

Reorder the terms:
ab + ax + b = b

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

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

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

Solving
ab + ax = 0

Solving for variable 'a'.

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

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

Solution

a = {0}

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