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Simplifying (2 + 3x)(4 + -1x) + -3x(3 + -1x) = 0 Multiply (2 + 3x) * (4 + -1x) (2(4 + -1x) + 3x * (4 + -1x)) + -3x(3 + -1x) = 0 ((4 * 2 + -1x * 2) + 3x * (4 + -1x)) + -3x(3 + -1x) = 0 ((8 + -2x) + 3x * (4 + -1x)) + -3x(3 + -1x) = 0 (8 + -2x + (4 * 3x + -1x * 3x)) + -3x(3 + -1x) = 0 (8 + -2x + (12x + -3x2)) + -3x(3 + -1x) = 0 Combine like terms: -2x + 12x = 10x (8 + 10x + -3x2) + -3x(3 + -1x) = 0 8 + 10x + -3x2 + (3 * -3x + -1x * -3x) = 0 8 + 10x + -3x2 + (-9x + 3x2) = 0 Reorder the terms: 8 + 10x + -9x + -3x2 + 3x2 = 0 Combine like terms: 10x + -9x = 1x 8 + 1x + -3x2 + 3x2 = 0 Combine like terms: -3x2 + 3x2 = 0 8 + 1x + 0 = 0 8 + 1x = 0 Solving 8 + 1x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 1x = 0 + -8 1x = 0 + -8 Combine like terms: 0 + -8 = -8 1x = -8 Divide each side by '1'. x = -8 Simplifying x = -8
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