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Simplifying b = (x + 5)(x + -7) + (3x + 1)(5 + -1x) Reorder the terms: b = (5 + x)(x + -7) + (3x + 1)(5 + -1x) Reorder the terms: b = (5 + x)(-7 + x) + (3x + 1)(5 + -1x) Multiply (5 + x) * (-7 + x) b = (5(-7 + x) + x(-7 + x)) + (3x + 1)(5 + -1x) b = ((-7 * 5 + x * 5) + x(-7 + x)) + (3x + 1)(5 + -1x) b = ((-35 + 5x) + x(-7 + x)) + (3x + 1)(5 + -1x) b = (-35 + 5x + (-7 * x + x * x)) + (3x + 1)(5 + -1x) b = (-35 + 5x + (-7x + x2)) + (3x + 1)(5 + -1x) Combine like terms: 5x + -7x = -2x b = (-35 + -2x + x2) + (3x + 1)(5 + -1x) Reorder the terms: b = -35 + -2x + x2 + (1 + 3x)(5 + -1x) Multiply (1 + 3x) * (5 + -1x) b = -35 + -2x + x2 + (1(5 + -1x) + 3x * (5 + -1x)) b = -35 + -2x + x2 + ((5 * 1 + -1x * 1) + 3x * (5 + -1x)) b = -35 + -2x + x2 + ((5 + -1x) + 3x * (5 + -1x)) b = -35 + -2x + x2 + (5 + -1x + (5 * 3x + -1x * 3x)) b = -35 + -2x + x2 + (5 + -1x + (15x + -3x2)) Combine like terms: -1x + 15x = 14x b = -35 + -2x + x2 + (5 + 14x + -3x2) Reorder the terms: b = -35 + 5 + -2x + 14x + x2 + -3x2 Combine like terms: -35 + 5 = -30 b = -30 + -2x + 14x + x2 + -3x2 Combine like terms: -2x + 14x = 12x b = -30 + 12x + x2 + -3x2 Combine like terms: x2 + -3x2 = -2x2 b = -30 + 12x + -2x2 Solving b = -30 + 12x + -2x2 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Simplifying b = -30 + 12x + -2x2
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