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Simplifying -8b2 + -1[-5b + -1(7b2 + -9b)] + -1[-3 + (20b + 3)] = 0 Reorder the terms: -8b2 + -1[-5b + -1(-9b + 7b2)] + -1[-3 + (20b + 3)] = 0 -8b2 + -1[-5b + (-9b * -1 + 7b2 * -1)] + -1[-3 + (20b + 3)] = 0 -8b2 + -1[-5b + (9b + -7b2)] + -1[-3 + (20b + 3)] = 0 Combine like terms: -5b + 9b = 4b -8b2 + -1[4b + -7b2] + -1[-3 + (20b + 3)] = 0 -8b2 + [4b * -1 + -7b2 * -1] + -1[-3 + (20b + 3)] = 0 -8b2 + [-4b + 7b2] + -1[-3 + (20b + 3)] = 0 Reorder the terms: -8b2 + -4b + 7b2 + -1[-3 + (3 + 20b)] = 0 Remove parenthesis around (3 + 20b) -8b2 + -4b + 7b2 + -1[-3 + 3 + 20b] = 0 Combine like terms: -3 + 3 = 0 -8b2 + -4b + 7b2 + -1[0 + 20b] = 0 -8b2 + -4b + 7b2 + -1[20b] = 0 Remove brackets around [20b] -8b2 + -4b + 7b2 + -1 * 20b = 0 Multiply -1 * 20 -8b2 + -4b + 7b2 + -20b = 0 Reorder the terms: -4b + -20b + -8b2 + 7b2 = 0 Combine like terms: -4b + -20b = -24b -24b + -8b2 + 7b2 = 0 Combine like terms: -8b2 + 7b2 = -1b2 -24b + -1b2 = 0 Solving -24b + -1b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '-1b'. -1b(24 + b) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(24 + b)' equal to zero and attempt to solve: Simplifying 24 + b = 0 Solving 24 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + b = 0 + -24 Combine like terms: 24 + -24 = 0 0 + b = 0 + -24 b = 0 + -24 Combine like terms: 0 + -24 = -24 b = -24 Simplifying b = -24Solution
b = {0, -24}
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