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Simplifying -3b(b + -8) + -5 = 9(b + 2) + -11 Reorder the terms: -3b(-8 + b) + -5 = 9(b + 2) + -11 (-8 * -3b + b * -3b) + -5 = 9(b + 2) + -11 (24b + -3b2) + -5 = 9(b + 2) + -11 Reorder the terms: -5 + 24b + -3b2 = 9(b + 2) + -11 Reorder the terms: -5 + 24b + -3b2 = 9(2 + b) + -11 -5 + 24b + -3b2 = (2 * 9 + b * 9) + -11 -5 + 24b + -3b2 = (18 + 9b) + -11 Reorder the terms: -5 + 24b + -3b2 = 18 + -11 + 9b Combine like terms: 18 + -11 = 7 -5 + 24b + -3b2 = 7 + 9b Solving -5 + 24b + -3b2 = 7 + 9b Solving for variable 'b'. Reorder the terms: -5 + -7 + 24b + -9b + -3b2 = 7 + 9b + -7 + -9b Combine like terms: -5 + -7 = -12 -12 + 24b + -9b + -3b2 = 7 + 9b + -7 + -9b Combine like terms: 24b + -9b = 15b -12 + 15b + -3b2 = 7 + 9b + -7 + -9b Reorder the terms: -12 + 15b + -3b2 = 7 + -7 + 9b + -9b Combine like terms: 7 + -7 = 0 -12 + 15b + -3b2 = 0 + 9b + -9b -12 + 15b + -3b2 = 9b + -9b Combine like terms: 9b + -9b = 0 -12 + 15b + -3b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 5b + -1b2) = 0 Factor a trinomial. 3((-4 + b)(1 + -1b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + b)' equal to zero and attempt to solve: Simplifying -4 + b = 0 Solving -4 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + b = 0 + 4 Combine like terms: -4 + 4 = 0 0 + b = 0 + 4 b = 0 + 4 Combine like terms: 0 + 4 = 4 b = 4 Simplifying b = 4Subproblem 2
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 = 1Solution
b = {4, 1}
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