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Simplifying 6(3x + 2) + 5(7x + -6) + -12x = 6(x + -3) + 5(6x + -1) Reorder the terms: 6(2 + 3x) + 5(7x + -6) + -12x = 6(x + -3) + 5(6x + -1) (2 * 6 + 3x * 6) + 5(7x + -6) + -12x = 6(x + -3) + 5(6x + -1) (12 + 18x) + 5(7x + -6) + -12x = 6(x + -3) + 5(6x + -1) Reorder the terms: 12 + 18x + 5(-6 + 7x) + -12x = 6(x + -3) + 5(6x + -1) 12 + 18x + (-6 * 5 + 7x * 5) + -12x = 6(x + -3) + 5(6x + -1) 12 + 18x + (-30 + 35x) + -12x = 6(x + -3) + 5(6x + -1) Reorder the terms: 12 + -30 + 18x + 35x + -12x = 6(x + -3) + 5(6x + -1) Combine like terms: 12 + -30 = -18 -18 + 18x + 35x + -12x = 6(x + -3) + 5(6x + -1) Combine like terms: 18x + 35x = 53x -18 + 53x + -12x = 6(x + -3) + 5(6x + -1) Combine like terms: 53x + -12x = 41x -18 + 41x = 6(x + -3) + 5(6x + -1) Reorder the terms: -18 + 41x = 6(-3 + x) + 5(6x + -1) -18 + 41x = (-3 * 6 + x * 6) + 5(6x + -1) -18 + 41x = (-18 + 6x) + 5(6x + -1) Reorder the terms: -18 + 41x = -18 + 6x + 5(-1 + 6x) -18 + 41x = -18 + 6x + (-1 * 5 + 6x * 5) -18 + 41x = -18 + 6x + (-5 + 30x) Reorder the terms: -18 + 41x = -18 + -5 + 6x + 30x Combine like terms: -18 + -5 = -23 -18 + 41x = -23 + 6x + 30x Combine like terms: 6x + 30x = 36x -18 + 41x = -23 + 36x Solving -18 + 41x = -23 + 36x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36x' to each side of the equation. -18 + 41x + -36x = -23 + 36x + -36x Combine like terms: 41x + -36x = 5x -18 + 5x = -23 + 36x + -36x Combine like terms: 36x + -36x = 0 -18 + 5x = -23 + 0 -18 + 5x = -23 Add '18' to each side of the equation. -18 + 18 + 5x = -23 + 18 Combine like terms: -18 + 18 = 0 0 + 5x = -23 + 18 5x = -23 + 18 Combine like terms: -23 + 18 = -5 5x = -5 Divide each side by '5'. x = -1 Simplifying x = -1
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