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Simplifying (2x + -3)(4 + -3x) = (x + -5)(7 + -6x) Reorder the terms: (-3 + 2x)(4 + -3x) = (x + -5)(7 + -6x) Multiply (-3 + 2x) * (4 + -3x) (-3(4 + -3x) + 2x * (4 + -3x)) = (x + -5)(7 + -6x) ((4 * -3 + -3x * -3) + 2x * (4 + -3x)) = (x + -5)(7 + -6x) ((-12 + 9x) + 2x * (4 + -3x)) = (x + -5)(7 + -6x) (-12 + 9x + (4 * 2x + -3x * 2x)) = (x + -5)(7 + -6x) (-12 + 9x + (8x + -6x2)) = (x + -5)(7 + -6x) Combine like terms: 9x + 8x = 17x (-12 + 17x + -6x2) = (x + -5)(7 + -6x) Reorder the terms: -12 + 17x + -6x2 = (-5 + x)(7 + -6x) Multiply (-5 + x) * (7 + -6x) -12 + 17x + -6x2 = (-5(7 + -6x) + x(7 + -6x)) -12 + 17x + -6x2 = ((7 * -5 + -6x * -5) + x(7 + -6x)) -12 + 17x + -6x2 = ((-35 + 30x) + x(7 + -6x)) -12 + 17x + -6x2 = (-35 + 30x + (7 * x + -6x * x)) -12 + 17x + -6x2 = (-35 + 30x + (7x + -6x2)) Combine like terms: 30x + 7x = 37x -12 + 17x + -6x2 = (-35 + 37x + -6x2) Add '6x2' to each side of the equation. -12 + 17x + -6x2 + 6x2 = -35 + 37x + -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -12 + 17x + 0 = -35 + 37x + -6x2 + 6x2 -12 + 17x = -35 + 37x + -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -12 + 17x = -35 + 37x + 0 -12 + 17x = -35 + 37x Solving -12 + 17x = -35 + 37x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37x' to each side of the equation. -12 + 17x + -37x = -35 + 37x + -37x Combine like terms: 17x + -37x = -20x -12 + -20x = -35 + 37x + -37x Combine like terms: 37x + -37x = 0 -12 + -20x = -35 + 0 -12 + -20x = -35 Add '12' to each side of the equation. -12 + 12 + -20x = -35 + 12 Combine like terms: -12 + 12 = 0 0 + -20x = -35 + 12 -20x = -35 + 12 Combine like terms: -35 + 12 = -23 -20x = -23 Divide each side by '-20'. x = 1.15 Simplifying x = 1.15
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