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Simplifying (x + 4)(3x + -7) = (x + -2)(3x + 8) Reorder the terms: (4 + x)(3x + -7) = (x + -2)(3x + 8) Reorder the terms: (4 + x)(-7 + 3x) = (x + -2)(3x + 8) Multiply (4 + x) * (-7 + 3x) (4(-7 + 3x) + x(-7 + 3x)) = (x + -2)(3x + 8) ((-7 * 4 + 3x * 4) + x(-7 + 3x)) = (x + -2)(3x + 8) ((-28 + 12x) + x(-7 + 3x)) = (x + -2)(3x + 8) (-28 + 12x + (-7 * x + 3x * x)) = (x + -2)(3x + 8) (-28 + 12x + (-7x + 3x2)) = (x + -2)(3x + 8) Combine like terms: 12x + -7x = 5x (-28 + 5x + 3x2) = (x + -2)(3x + 8) Reorder the terms: -28 + 5x + 3x2 = (-2 + x)(3x + 8) Reorder the terms: -28 + 5x + 3x2 = (-2 + x)(8 + 3x) Multiply (-2 + x) * (8 + 3x) -28 + 5x + 3x2 = (-2(8 + 3x) + x(8 + 3x)) -28 + 5x + 3x2 = ((8 * -2 + 3x * -2) + x(8 + 3x)) -28 + 5x + 3x2 = ((-16 + -6x) + x(8 + 3x)) -28 + 5x + 3x2 = (-16 + -6x + (8 * x + 3x * x)) -28 + 5x + 3x2 = (-16 + -6x + (8x + 3x2)) Combine like terms: -6x + 8x = 2x -28 + 5x + 3x2 = (-16 + 2x + 3x2) Add '-3x2' to each side of the equation. -28 + 5x + 3x2 + -3x2 = -16 + 2x + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -28 + 5x + 0 = -16 + 2x + 3x2 + -3x2 -28 + 5x = -16 + 2x + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -28 + 5x = -16 + 2x + 0 -28 + 5x = -16 + 2x Solving -28 + 5x = -16 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -28 + 5x + -2x = -16 + 2x + -2x Combine like terms: 5x + -2x = 3x -28 + 3x = -16 + 2x + -2x Combine like terms: 2x + -2x = 0 -28 + 3x = -16 + 0 -28 + 3x = -16 Add '28' to each side of the equation. -28 + 28 + 3x = -16 + 28 Combine like terms: -28 + 28 = 0 0 + 3x = -16 + 28 3x = -16 + 28 Combine like terms: -16 + 28 = 12 3x = 12 Divide each side by '3'. x = 4 Simplifying x = 4
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