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Simplifying (x + 1)(-6x + 12) = (2x + -1)(-3x + 6) Reorder the terms: (1 + x)(-6x + 12) = (2x + -1)(-3x + 6) Reorder the terms: (1 + x)(12 + -6x) = (2x + -1)(-3x + 6) Multiply (1 + x) * (12 + -6x) (1(12 + -6x) + x(12 + -6x)) = (2x + -1)(-3x + 6) ((12 * 1 + -6x * 1) + x(12 + -6x)) = (2x + -1)(-3x + 6) ((12 + -6x) + x(12 + -6x)) = (2x + -1)(-3x + 6) (12 + -6x + (12 * x + -6x * x)) = (2x + -1)(-3x + 6) (12 + -6x + (12x + -6x2)) = (2x + -1)(-3x + 6) Combine like terms: -6x + 12x = 6x (12 + 6x + -6x2) = (2x + -1)(-3x + 6) Reorder the terms: 12 + 6x + -6x2 = (-1 + 2x)(-3x + 6) Reorder the terms: 12 + 6x + -6x2 = (-1 + 2x)(6 + -3x) Multiply (-1 + 2x) * (6 + -3x) 12 + 6x + -6x2 = (-1(6 + -3x) + 2x * (6 + -3x)) 12 + 6x + -6x2 = ((6 * -1 + -3x * -1) + 2x * (6 + -3x)) 12 + 6x + -6x2 = ((-6 + 3x) + 2x * (6 + -3x)) 12 + 6x + -6x2 = (-6 + 3x + (6 * 2x + -3x * 2x)) 12 + 6x + -6x2 = (-6 + 3x + (12x + -6x2)) Combine like terms: 3x + 12x = 15x 12 + 6x + -6x2 = (-6 + 15x + -6x2) Add '6x2' to each side of the equation. 12 + 6x + -6x2 + 6x2 = -6 + 15x + -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 12 + 6x + 0 = -6 + 15x + -6x2 + 6x2 12 + 6x = -6 + 15x + -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 12 + 6x = -6 + 15x + 0 12 + 6x = -6 + 15x Solving 12 + 6x = -6 + 15x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15x' to each side of the equation. 12 + 6x + -15x = -6 + 15x + -15x Combine like terms: 6x + -15x = -9x 12 + -9x = -6 + 15x + -15x Combine like terms: 15x + -15x = 0 12 + -9x = -6 + 0 12 + -9x = -6 Add '-12' to each side of the equation. 12 + -12 + -9x = -6 + -12 Combine like terms: 12 + -12 = 0 0 + -9x = -6 + -12 -9x = -6 + -12 Combine like terms: -6 + -12 = -18 -9x = -18 Divide each side by '-9'. x = 2 Simplifying x = 2
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