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Simplifying (3x + -5)(7 + 4x) = (6x + -2)(5 + 2x) Reorder the terms: (-5 + 3x)(7 + 4x) = (6x + -2)(5 + 2x) Multiply (-5 + 3x) * (7 + 4x) (-5(7 + 4x) + 3x * (7 + 4x)) = (6x + -2)(5 + 2x) ((7 * -5 + 4x * -5) + 3x * (7 + 4x)) = (6x + -2)(5 + 2x) ((-35 + -20x) + 3x * (7 + 4x)) = (6x + -2)(5 + 2x) (-35 + -20x + (7 * 3x + 4x * 3x)) = (6x + -2)(5 + 2x) (-35 + -20x + (21x + 12x2)) = (6x + -2)(5 + 2x) Combine like terms: -20x + 21x = 1x (-35 + 1x + 12x2) = (6x + -2)(5 + 2x) Reorder the terms: -35 + 1x + 12x2 = (-2 + 6x)(5 + 2x) Multiply (-2 + 6x) * (5 + 2x) -35 + 1x + 12x2 = (-2(5 + 2x) + 6x * (5 + 2x)) -35 + 1x + 12x2 = ((5 * -2 + 2x * -2) + 6x * (5 + 2x)) -35 + 1x + 12x2 = ((-10 + -4x) + 6x * (5 + 2x)) -35 + 1x + 12x2 = (-10 + -4x + (5 * 6x + 2x * 6x)) -35 + 1x + 12x2 = (-10 + -4x + (30x + 12x2)) Combine like terms: -4x + 30x = 26x -35 + 1x + 12x2 = (-10 + 26x + 12x2) Add '-12x2' to each side of the equation. -35 + 1x + 12x2 + -12x2 = -10 + 26x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -35 + 1x + 0 = -10 + 26x + 12x2 + -12x2 -35 + 1x = -10 + 26x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -35 + 1x = -10 + 26x + 0 -35 + 1x = -10 + 26x Solving -35 + 1x = -10 + 26x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26x' to each side of the equation. -35 + 1x + -26x = -10 + 26x + -26x Combine like terms: 1x + -26x = -25x -35 + -25x = -10 + 26x + -26x Combine like terms: 26x + -26x = 0 -35 + -25x = -10 + 0 -35 + -25x = -10 Add '35' to each side of the equation. -35 + 35 + -25x = -10 + 35 Combine like terms: -35 + 35 = 0 0 + -25x = -10 + 35 -25x = -10 + 35 Combine like terms: -10 + 35 = 25 -25x = 25 Divide each side by '-25'. x = -1 Simplifying x = -1
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