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Simplifying (3 + 3i)(3 + -3i)(x + -6) = 0 Reorder the terms: (3 + 3i)(3 + -3i)(-6 + x) = 0 Multiply (3 + 3i) * (3 + -3i) (3(3 + -3i) + 3i * (3 + -3i))(-6 + x) = 0 ((3 * 3 + -3i * 3) + 3i * (3 + -3i))(-6 + x) = 0 ((9 + -9i) + 3i * (3 + -3i))(-6 + x) = 0 (9 + -9i + (3 * 3i + -3i * 3i))(-6 + x) = 0 (9 + -9i + (9i + -9i2))(-6 + x) = 0 Combine like terms: -9i + 9i = 0 (9 + 0 + -9i2)(-6 + x) = 0 (9 + -9i2)(-6 + x) = 0 Multiply (9 + -9i2) * (-6 + x) (9(-6 + x) + -9i2 * (-6 + x)) = 0 ((-6 * 9 + x * 9) + -9i2 * (-6 + x)) = 0 ((-54 + 9x) + -9i2 * (-6 + x)) = 0 (-54 + 9x + (-6 * -9i2 + x * -9i2)) = 0 (-54 + 9x + (54i2 + -9i2x)) = 0 Reorder the terms: (-54 + 54i2 + -9i2x + 9x) = 0 (-54 + 54i2 + -9i2x + 9x) = 0 Solving -54 + 54i2 + -9i2x + 9x = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54i2 + -9i2x + 54 + 9x = 0 + 54 Reorder the terms: -54 + 54 + 54i2 + -9i2x + 9x = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 54i2 + -9i2x + 9x = 0 + 54 54i2 + -9i2x + 9x = 0 + 54 Combine like terms: 0 + 54 = 54 54i2 + -9i2x + 9x = 54 Add '-9x' to each side of the equation. 54i2 + -9i2x + 9x + -9x = 54 + -9x Combine like terms: 9x + -9x = 0 54i2 + -9i2x + 0 = 54 + -9x 54i2 + -9i2x = 54 + -9x Reorder the terms: -54 + 54i2 + -9i2x + 9x = 54 + -9x + -54 + 9x Reorder the terms: -54 + 54i2 + -9i2x + 9x = 54 + -54 + -9x + 9x Combine like terms: 54 + -54 = 0 -54 + 54i2 + -9i2x + 9x = 0 + -9x + 9x -54 + 54i2 + -9i2x + 9x = -9x + 9x Combine like terms: -9x + 9x = 0 -54 + 54i2 + -9i2x + 9x = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-6 + 6i2 + -1i2x + x) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-6 + 6i2 + -1i2x + x)' equal to zero and attempt to solve: Simplifying -6 + 6i2 + -1i2x + x = 0 Solving -6 + 6i2 + -1i2x + x = 0 Move all terms containing i to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6i2 + -1i2x + 6 + x = 0 + 6 Reorder the terms: -6 + 6 + 6i2 + -1i2x + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 6i2 + -1i2x + x = 0 + 6 6i2 + -1i2x + x = 0 + 6 Combine like terms: 0 + 6 = 6 6i2 + -1i2x + x = 6 Add '-1x' to each side of the equation. 6i2 + -1i2x + x + -1x = 6 + -1x Combine like terms: x + -1x = 0 6i2 + -1i2x + 0 = 6 + -1x 6i2 + -1i2x = 6 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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