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Simplifying a(a + b + c) = 0 (a * a + b * a + c * a) = 0 Reorder the terms: (ab + ac + a2) = 0 (ab + ac + a2) = 0 Solving ab + ac + a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(b + c + a) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(b + c + a)' equal to zero and attempt to solve: Simplifying b + c + a = 0 Reorder the terms: a + b + c = 0 Solving a + b + c = 0 Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. a + b + -1b + c = 0 + -1b Combine like terms: b + -1b = 0 a + 0 + c = 0 + -1b a + c = 0 + -1b Remove the zero: a + c = -1b Add '-1c' to each side of the equation. a + c + -1c = -1b + -1c Combine like terms: c + -1c = 0 a + 0 = -1b + -1c a = -1b + -1c Simplifying a = -1b + -1cSolution
a = {0, -1b + -1c}
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