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Simplifying 5b2 + 10b + -20 = -5b Reorder the terms: -20 + 10b + 5b2 = -5b Solving -20 + 10b + 5b2 = -5b Solving for variable 'b'. Reorder the terms: -20 + 10b + 5b + 5b2 = -5b + 5b Combine like terms: 10b + 5b = 15b -20 + 15b + 5b2 = -5b + 5b Combine like terms: -5b + 5b = 0 -20 + 15b + 5b2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-4 + 3b + b2) = 0 Factor a trinomial. 5((-4 + -1b)(1 + -1b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve: Simplifying -4 + -1b = 0 Solving -4 + -1b = 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 + -1b = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1b = 0 + 4 -1b = 0 + 4 Combine like terms: 0 + 4 = 4 -1b = 4 Divide each side by '-1'. 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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