AB+AB=AB+AC

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Solution for AB+AB=AB+AC equation:


Simplifying
AB + AB = AB + AC

Combine like terms: AB + AB = 2AB
2AB = AB + AC

Solving
2AB = AB + AC

Solving for variable 'A'.

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

Add '-1AB' to each side of the equation.
2AB + -1AB = AB + -1AB + AC

Combine like terms: 2AB + -1AB = 1AB
1AB = AB + -1AB + AC

Combine like terms: AB + -1AB = 0
1AB = 0 + AC
1AB = AC

Add '-1AC' to each side of the equation.
1AB + -1AC = AC + -1AC

Combine like terms: AC + -1AC = 0
1AB + -1AC = 0

Factor out the Greatest Common Factor (GCF), 'A'.
A(B + -1C) = 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 + -1C)' equal to zero and attempt to solve: Simplifying B + -1C = 0 Solving B + -1C = 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 + -1C = 0 + -1B Combine like terms: B + -1B = 0 0 + -1C = 0 + -1B -1C = 0 + -1B Remove the zero: -1C = -1B Add 'C' to each side of the equation. -1C + C = -1B + C Combine like terms: -1C + C = 0 0 = -1B + C Simplifying 0 = -1B + C 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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