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Simplifying (x + -3)(x + -5) = (x + 9)(x + 4) Reorder the terms: (-3 + x)(x + -5) = (x + 9)(x + 4) Reorder the terms: (-3 + x)(-5 + x) = (x + 9)(x + 4) Multiply (-3 + x) * (-5 + x) (-3(-5 + x) + x(-5 + x)) = (x + 9)(x + 4) ((-5 * -3 + x * -3) + x(-5 + x)) = (x + 9)(x + 4) ((15 + -3x) + x(-5 + x)) = (x + 9)(x + 4) (15 + -3x + (-5 * x + x * x)) = (x + 9)(x + 4) (15 + -3x + (-5x + x2)) = (x + 9)(x + 4) Combine like terms: -3x + -5x = -8x (15 + -8x + x2) = (x + 9)(x + 4) Reorder the terms: 15 + -8x + x2 = (9 + x)(x + 4) Reorder the terms: 15 + -8x + x2 = (9 + x)(4 + x) Multiply (9 + x) * (4 + x) 15 + -8x + x2 = (9(4 + x) + x(4 + x)) 15 + -8x + x2 = ((4 * 9 + x * 9) + x(4 + x)) 15 + -8x + x2 = ((36 + 9x) + x(4 + x)) 15 + -8x + x2 = (36 + 9x + (4 * x + x * x)) 15 + -8x + x2 = (36 + 9x + (4x + x2)) Combine like terms: 9x + 4x = 13x 15 + -8x + x2 = (36 + 13x + x2) Add '-1x2' to each side of the equation. 15 + -8x + x2 + -1x2 = 36 + 13x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + -8x + 0 = 36 + 13x + x2 + -1x2 15 + -8x = 36 + 13x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + -8x = 36 + 13x + 0 15 + -8x = 36 + 13x Solving 15 + -8x = 36 + 13x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13x' to each side of the equation. 15 + -8x + -13x = 36 + 13x + -13x Combine like terms: -8x + -13x = -21x 15 + -21x = 36 + 13x + -13x Combine like terms: 13x + -13x = 0 15 + -21x = 36 + 0 15 + -21x = 36 Add '-15' to each side of the equation. 15 + -15 + -21x = 36 + -15 Combine like terms: 15 + -15 = 0 0 + -21x = 36 + -15 -21x = 36 + -15 Combine like terms: 36 + -15 = 21 -21x = 21 Divide each side by '-21'. x = -1 Simplifying x = -1
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