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Simplifying (a + 3b) + (3a + -1b) * i = 6 + 6i Remove parenthesis around (a + 3b) a + 3b + (3a + -1b) * i = 6 + 6i Reorder the terms for easier multiplication: a + 3b + i(3a + -1b) = 6 + 6i a + 3b + (3a * i + -1b * i) = 6 + 6i a + 3b + (3ai + -1bi) = 6 + 6i Reorder the terms: a + 3ai + 3b + -1bi = 6 + 6i Solving a + 3ai + 3b + -1bi = 6 + 6i Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. a + 3ai + 3b + -3b + -1bi = 6 + -3b + 6i Combine like terms: 3b + -3b = 0 a + 3ai + 0 + -1bi = 6 + -3b + 6i a + 3ai + -1bi = 6 + -3b + 6i Add 'bi' to each side of the equation. a + 3ai + -1bi + bi = 6 + -3b + bi + 6i Combine like terms: -1bi + bi = 0 a + 3ai + 0 = 6 + -3b + bi + 6i a + 3ai = 6 + -3b + bi + 6i Reorder the terms: -6 + a + 3ai + 3b + -1bi + -6i = 6 + -3b + bi + 6i + -6 + 3b + -1bi + -6i Reorder the terms: -6 + a + 3ai + 3b + -1bi + -6i = 6 + -6 + -3b + 3b + bi + -1bi + 6i + -6i Combine like terms: 6 + -6 = 0 -6 + a + 3ai + 3b + -1bi + -6i = 0 + -3b + 3b + bi + -1bi + 6i + -6i -6 + a + 3ai + 3b + -1bi + -6i = -3b + 3b + bi + -1bi + 6i + -6i Combine like terms: -3b + 3b = 0 -6 + a + 3ai + 3b + -1bi + -6i = 0 + bi + -1bi + 6i + -6i -6 + a + 3ai + 3b + -1bi + -6i = bi + -1bi + 6i + -6i Combine like terms: bi + -1bi = 0 -6 + a + 3ai + 3b + -1bi + -6i = 0 + 6i + -6i -6 + a + 3ai + 3b + -1bi + -6i = 6i + -6i Combine like terms: 6i + -6i = 0 -6 + a + 3ai + 3b + -1bi + -6i = 0 The solution to this equation could not be determined.
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