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Simplifying 21(b + -1) + 9 = 3(7b + -4) * b Reorder the terms: 21(-1 + b) + 9 = 3(7b + -4) * b (-1 * 21 + b * 21) + 9 = 3(7b + -4) * b (-21 + 21b) + 9 = 3(7b + -4) * b Reorder the terms: -21 + 9 + 21b = 3(7b + -4) * b Combine like terms: -21 + 9 = -12 -12 + 21b = 3(7b + -4) * b Reorder the terms: -12 + 21b = 3(-4 + 7b) * b Reorder the terms for easier multiplication: -12 + 21b = 3b(-4 + 7b) -12 + 21b = (-4 * 3b + 7b * 3b) -12 + 21b = (-12b + 21b2) Solving -12 + 21b = -12b + 21b2 Solving for variable 'b'. Combine like terms: 21b + 12b = 33b -12 + 33b + -21b2 = -12b + 21b2 + 12b + -21b2 Reorder the terms: -12 + 33b + -21b2 = -12b + 12b + 21b2 + -21b2 Combine like terms: -12b + 12b = 0 -12 + 33b + -21b2 = 0 + 21b2 + -21b2 -12 + 33b + -21b2 = 21b2 + -21b2 Combine like terms: 21b2 + -21b2 = 0 -12 + 33b + -21b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 11b + -7b2) = 0 Factor a trinomial. 3((-1 + b)(4 + -7b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + b)' equal to zero and attempt to solve: Simplifying -1 + b = 0 Solving -1 + b = 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 + b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + b = 0 + 1 b = 0 + 1 Combine like terms: 0 + 1 = 1 b = 1 Simplifying b = 1Subproblem 2
Set the factor '(4 + -7b)' equal to zero and attempt to solve: Simplifying 4 + -7b = 0 Solving 4 + -7b = 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 + -7b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7b = 0 + -4 -7b = 0 + -4 Combine like terms: 0 + -4 = -4 -7b = -4 Divide each side by '-7'. b = 0.5714285714 Simplifying b = 0.5714285714Solution
b = {1, 0.5714285714}
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