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Simplifying (3x + 2)(2x + -6) = (4 + -3x)(1 + -2x) + -1 Reorder the terms: (2 + 3x)(2x + -6) = (4 + -3x)(1 + -2x) + -1 Reorder the terms: (2 + 3x)(-6 + 2x) = (4 + -3x)(1 + -2x) + -1 Multiply (2 + 3x) * (-6 + 2x) (2(-6 + 2x) + 3x * (-6 + 2x)) = (4 + -3x)(1 + -2x) + -1 ((-6 * 2 + 2x * 2) + 3x * (-6 + 2x)) = (4 + -3x)(1 + -2x) + -1 ((-12 + 4x) + 3x * (-6 + 2x)) = (4 + -3x)(1 + -2x) + -1 (-12 + 4x + (-6 * 3x + 2x * 3x)) = (4 + -3x)(1 + -2x) + -1 (-12 + 4x + (-18x + 6x2)) = (4 + -3x)(1 + -2x) + -1 Combine like terms: 4x + -18x = -14x (-12 + -14x + 6x2) = (4 + -3x)(1 + -2x) + -1 Multiply (4 + -3x) * (1 + -2x) -12 + -14x + 6x2 = (4(1 + -2x) + -3x * (1 + -2x)) + -1 -12 + -14x + 6x2 = ((1 * 4 + -2x * 4) + -3x * (1 + -2x)) + -1 -12 + -14x + 6x2 = ((4 + -8x) + -3x * (1 + -2x)) + -1 -12 + -14x + 6x2 = (4 + -8x + (1 * -3x + -2x * -3x)) + -1 -12 + -14x + 6x2 = (4 + -8x + (-3x + 6x2)) + -1 Combine like terms: -8x + -3x = -11x -12 + -14x + 6x2 = (4 + -11x + 6x2) + -1 Reorder the terms: -12 + -14x + 6x2 = 4 + -1 + -11x + 6x2 Combine like terms: 4 + -1 = 3 -12 + -14x + 6x2 = 3 + -11x + 6x2 Add '-6x2' to each side of the equation. -12 + -14x + 6x2 + -6x2 = 3 + -11x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -12 + -14x + 0 = 3 + -11x + 6x2 + -6x2 -12 + -14x = 3 + -11x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -12 + -14x = 3 + -11x + 0 -12 + -14x = 3 + -11x Solving -12 + -14x = 3 + -11x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11x' to each side of the equation. -12 + -14x + 11x = 3 + -11x + 11x Combine like terms: -14x + 11x = -3x -12 + -3x = 3 + -11x + 11x Combine like terms: -11x + 11x = 0 -12 + -3x = 3 + 0 -12 + -3x = 3 Add '12' to each side of the equation. -12 + 12 + -3x = 3 + 12 Combine like terms: -12 + 12 = 0 0 + -3x = 3 + 12 -3x = 3 + 12 Combine like terms: 3 + 12 = 15 -3x = 15 Divide each side by '-3'. x = -5 Simplifying x = -5
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