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Simplifying 5 = 1 + -1(b + -1)(3b + 5) Reorder the terms: 5 = 1 + -1(-1 + b)(3b + 5) Reorder the terms: 5 = 1 + -1(-1 + b)(5 + 3b) Multiply (-1 + b) * (5 + 3b) 5 = 1 + -1(-1(5 + 3b) + b(5 + 3b)) 5 = 1 + -1((5 * -1 + 3b * -1) + b(5 + 3b)) 5 = 1 + -1((-5 + -3b) + b(5 + 3b)) 5 = 1 + -1(-5 + -3b + (5 * b + 3b * b)) 5 = 1 + -1(-5 + -3b + (5b + 3b2)) Combine like terms: -3b + 5b = 2b 5 = 1 + -1(-5 + 2b + 3b2) 5 = 1 + (-5 * -1 + 2b * -1 + 3b2 * -1) 5 = 1 + (5 + -2b + -3b2) Combine like terms: 1 + 5 = 6 5 = 6 + -2b + -3b2 Solving 5 = 6 + -2b + -3b2 Solving for variable 'b'. Combine like terms: 5 + -6 = -1 -1 + 2b + 3b2 = 6 + -2b + -3b2 + -6 + 2b + 3b2 Reorder the terms: -1 + 2b + 3b2 = 6 + -6 + -2b + 2b + -3b2 + 3b2 Combine like terms: 6 + -6 = 0 -1 + 2b + 3b2 = 0 + -2b + 2b + -3b2 + 3b2 -1 + 2b + 3b2 = -2b + 2b + -3b2 + 3b2 Combine like terms: -2b + 2b = 0 -1 + 2b + 3b2 = 0 + -3b2 + 3b2 -1 + 2b + 3b2 = -3b2 + 3b2 Combine like terms: -3b2 + 3b2 = 0 -1 + 2b + 3b2 = 0 Factor a trinomial. (-1 + -1b)(1 + -3b) = 0Subproblem 1
Set the factor '(-1 + -1b)' equal to zero and attempt to solve: Simplifying -1 + -1b = 0 Solving -1 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1b = 0 + 1 -1b = 0 + 1 Combine like terms: 0 + 1 = 1 -1b = 1 Divide each side by '-1'. b = -1 Simplifying b = -1Subproblem 2
Set the factor '(1 + -3b)' equal to zero and attempt to solve: Simplifying 1 + -3b = 0 Solving 1 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3b = 0 + -1 -3b = 0 + -1 Combine like terms: 0 + -1 = -1 -3b = -1 Divide each side by '-3'. b = 0.3333333333 Simplifying b = 0.3333333333Solution
b = {-1, 0.3333333333}
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