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Simplifying 3b2 = 45 + -6b Solving 3b2 = 45 + -6b Solving for variable 'b'. Reorder the terms: -45 + 6b + 3b2 = 45 + -6b + -45 + 6b Reorder the terms: -45 + 6b + 3b2 = 45 + -45 + -6b + 6b Combine like terms: 45 + -45 = 0 -45 + 6b + 3b2 = 0 + -6b + 6b -45 + 6b + 3b2 = -6b + 6b Combine like terms: -6b + 6b = 0 -45 + 6b + 3b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 2b + b2) = 0 Factor a trinomial. 3((-5 + -1b)(3 + -1b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + -1b)' equal to zero and attempt to solve: Simplifying -5 + -1b = 0 Solving -5 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1b = 0 + 5 -1b = 0 + 5 Combine like terms: 0 + 5 = 5 -1b = 5 Divide each side by '-1'. b = -5 Simplifying b = -5Subproblem 2
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 = 3Solution
b = {-5, 3}
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