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Simplifying (x + 3)(x + -1)(-3i) = 0 Reorder the terms: (3 + x)(x + -1)(-3i) = 0 Reorder the terms: (3 + x)(-1 + x)(-3i) = 0 Remove parenthesis around (-3i) (3 + x)(-1 + x) * -3i = 0 Reorder the terms for easier multiplication: -3i(3 + x)(-1 + x) = 0 Multiply (3 + x) * (-1 + x) -3i(3(-1 + x) + x(-1 + x)) = 0 -3i((-1 * 3 + x * 3) + x(-1 + x)) = 0 -3i((-3 + 3x) + x(-1 + x)) = 0 -3i(-3 + 3x + (-1 * x + x * x)) = 0 -3i(-3 + 3x + (-1x + x2)) = 0 Combine like terms: 3x + -1x = 2x -3i(-3 + 2x + x2) = 0 (-3 * -3i + 2x * -3i + x2 * -3i) = 0 (9i + -6ix + -3ix2) = 0 Solving 9i + -6ix + -3ix2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '3i'. 3i(3 + -2x + -1x2) = 0 Factor a trinomial. 3i((1 + -1x)(3 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
i = {0}
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