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Simplifying 0 = -5b2 + 30 + -5b Reorder the terms: 0 = 30 + -5b + -5b2 Solving 0 = 30 + -5b + -5b2 Solving for variable 'b'. Combine like terms: 0 + -30 = -30 -30 + 5b + 5b2 = 30 + -5b + -5b2 + -30 + 5b + 5b2 Reorder the terms: -30 + 5b + 5b2 = 30 + -30 + -5b + 5b + -5b2 + 5b2 Combine like terms: 30 + -30 = 0 -30 + 5b + 5b2 = 0 + -5b + 5b + -5b2 + 5b2 -30 + 5b + 5b2 = -5b + 5b + -5b2 + 5b2 Combine like terms: -5b + 5b = 0 -30 + 5b + 5b2 = 0 + -5b2 + 5b2 -30 + 5b + 5b2 = -5b2 + 5b2 Combine like terms: -5b2 + 5b2 = 0 -30 + 5b + 5b2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + b + b2) = 0 Factor a trinomial. 5((-3 + -1b)(2 + -1b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -1b)' equal to zero and attempt to solve: Simplifying -3 + -1b = 0 Solving -3 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b = 0 + 3 -1b = 0 + 3 Combine like terms: 0 + 3 = 3 -1b = 3 Divide each side by '-1'. b = -3 Simplifying b = -3Subproblem 2
Set the factor '(2 + -1b)' equal to zero and attempt to solve: Simplifying 2 + -1b = 0 Solving 2 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1b = 0 + -2 -1b = 0 + -2 Combine like terms: 0 + -2 = -2 -1b = -2 Divide each side by '-1'. b = 2 Simplifying b = 2Solution
b = {-3, 2}
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