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Simplifying (b + -7)(b + 5) = (b + 8)(b + -9) Reorder the terms: (-7 + b)(b + 5) = (b + 8)(b + -9) Reorder the terms: (-7 + b)(5 + b) = (b + 8)(b + -9) Multiply (-7 + b) * (5 + b) (-7(5 + b) + b(5 + b)) = (b + 8)(b + -9) ((5 * -7 + b * -7) + b(5 + b)) = (b + 8)(b + -9) ((-35 + -7b) + b(5 + b)) = (b + 8)(b + -9) (-35 + -7b + (5 * b + b * b)) = (b + 8)(b + -9) (-35 + -7b + (5b + b2)) = (b + 8)(b + -9) Combine like terms: -7b + 5b = -2b (-35 + -2b + b2) = (b + 8)(b + -9) Reorder the terms: -35 + -2b + b2 = (8 + b)(b + -9) Reorder the terms: -35 + -2b + b2 = (8 + b)(-9 + b) Multiply (8 + b) * (-9 + b) -35 + -2b + b2 = (8(-9 + b) + b(-9 + b)) -35 + -2b + b2 = ((-9 * 8 + b * 8) + b(-9 + b)) -35 + -2b + b2 = ((-72 + 8b) + b(-9 + b)) -35 + -2b + b2 = (-72 + 8b + (-9 * b + b * b)) -35 + -2b + b2 = (-72 + 8b + (-9b + b2)) Combine like terms: 8b + -9b = -1b -35 + -2b + b2 = (-72 + -1b + b2) Add '-1b2' to each side of the equation. -35 + -2b + b2 + -1b2 = -72 + -1b + b2 + -1b2 Combine like terms: b2 + -1b2 = 0 -35 + -2b + 0 = -72 + -1b + b2 + -1b2 -35 + -2b = -72 + -1b + b2 + -1b2 Combine like terms: b2 + -1b2 = 0 -35 + -2b = -72 + -1b + 0 -35 + -2b = -72 + -1b Solving -35 + -2b = -72 + -1b Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add 'b' to each side of the equation. -35 + -2b + b = -72 + -1b + b Combine like terms: -2b + b = -1b -35 + -1b = -72 + -1b + b Combine like terms: -1b + b = 0 -35 + -1b = -72 + 0 -35 + -1b = -72 Add '35' to each side of the equation. -35 + 35 + -1b = -72 + 35 Combine like terms: -35 + 35 = 0 0 + -1b = -72 + 35 -1b = -72 + 35 Combine like terms: -72 + 35 = -37 -1b = -37 Divide each side by '-1'. b = 37 Simplifying b = 37
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