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Simplifying A(X + 3)(X + -3I + 1) = 0 Reorder the terms: A(3 + X)(X + -3I + 1) = 0 Reorder the terms: A(3 + X)(1 + -3I + X) = 0 Multiply (3 + X) * (1 + -3I + X) A(3(1 + -3I + X) + X(1 + -3I + X)) = 0 A((1 * 3 + -3I * 3 + X * 3) + X(1 + -3I + X)) = 0 A((3 + -9I + 3X) + X(1 + -3I + X)) = 0 A(3 + -9I + 3X + (1 * X + -3I * X + X * X)) = 0 Reorder the terms: A(3 + -9I + 3X + (-3IX + 1X + X2)) = 0 A(3 + -9I + 3X + (-3IX + 1X + X2)) = 0 Reorder the terms: A(3 + -9I + -3IX + 3X + 1X + X2) = 0 Combine like terms: 3X + 1X = 4X A(3 + -9I + -3IX + 4X + X2) = 0 (3 * A + -9I * A + -3IX * A + 4X * A + X2 * A) = 0 (3A + -9AI + -3AIX + 4AX + AX2) = 0 Solving 3A + -9AI + -3AIX + 4AX + AX2 = 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(3 + -9I + -3IX + 4X + X2) = 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 '(3 + -9I + -3IX + 4X + X2)' equal to zero and attempt to solve: Simplifying 3 + -9I + -3IX + 4X + X2 = 0 Solving 3 + -9I + -3IX + 4X + X2 = 0 Move all terms containing A to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -9I + -3IX + 4X + -3 + X2 = 0 + -3 Reorder the terms: 3 + -3 + -9I + -3IX + 4X + X2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -9I + -3IX + 4X + X2 = 0 + -3 -9I + -3IX + 4X + X2 = 0 + -3 Combine like terms: 0 + -3 = -3 -9I + -3IX + 4X + X2 = -3 Add '9I' to each side of the equation. -9I + -3IX + 4X + 9I + X2 = -3 + 9I Reorder the terms: -9I + 9I + -3IX + 4X + X2 = -3 + 9I Combine like terms: -9I + 9I = 0 0 + -3IX + 4X + X2 = -3 + 9I -3IX + 4X + X2 = -3 + 9I Add '3IX' to each side of the equation. -3IX + 4X + 3IX + X2 = -3 + 9I + 3IX Reorder the terms: -3IX + 3IX + 4X + X2 = -3 + 9I + 3IX Combine like terms: -3IX + 3IX = 0 0 + 4X + X2 = -3 + 9I + 3IX 4X + X2 = -3 + 9I + 3IX Add '-4X' to each side of the equation. 4X + -4X + X2 = -3 + 9I + 3IX + -4X Combine like terms: 4X + -4X = 0 0 + X2 = -3 + 9I + 3IX + -4X X2 = -3 + 9I + 3IX + -4X Add '-1X2' to each side of the equation. X2 + -1X2 = -3 + 9I + 3IX + -4X + -1X2 Combine like terms: X2 + -1X2 = 0 0 = -3 + 9I + 3IX + -4X + -1X2 Simplifying 0 = -3 + 9I + 3IX + -4X + -1X2 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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