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Simplifying 12(2x + 3) + -3(i + 7x) = 0 Reorder the terms: 12(3 + 2x) + -3(i + 7x) = 0 (3 * 12 + 2x * 12) + -3(i + 7x) = 0 (36 + 24x) + -3(i + 7x) = 0 36 + 24x + (i * -3 + 7x * -3) = 0 36 + 24x + (-3i + -21x) = 0 Reorder the terms: 36 + -3i + 24x + -21x = 0 Combine like terms: 24x + -21x = 3x 36 + -3i + 3x = 0 Solving 36 + -3i + 3x = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -3i + -36 + 3x = 0 + -36 Reorder the terms: 36 + -36 + -3i + 3x = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -3i + 3x = 0 + -36 -3i + 3x = 0 + -36 Combine like terms: 0 + -36 = -36 -3i + 3x = -36 Add '-3x' to each side of the equation. -3i + 3x + -3x = -36 + -3x Combine like terms: 3x + -3x = 0 -3i + 0 = -36 + -3x -3i = -36 + -3x Divide each side by '-3'. i = 12 + x Simplifying i = 12 + x
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