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Simplifying 6b2 = 18 + 3b Solving 6b2 = 18 + 3b Solving for variable 'b'. Reorder the terms: -18 + -3b + 6b2 = 18 + 3b + -18 + -3b Reorder the terms: -18 + -3b + 6b2 = 18 + -18 + 3b + -3b Combine like terms: 18 + -18 = 0 -18 + -3b + 6b2 = 0 + 3b + -3b -18 + -3b + 6b2 = 3b + -3b Combine like terms: 3b + -3b = 0 -18 + -3b + 6b2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + -1b + 2b2) = 0 Factor a trinomial. 3((-3 + -2b)(2 + -1b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-3 + -2b)' equal to zero and attempt to solve: Simplifying -3 + -2b = 0 Solving -3 + -2b = 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 + -2b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2b = 0 + 3 -2b = 0 + 3 Combine like terms: 0 + 3 = 3 -2b = 3 Divide each side by '-2'. b = -1.5 Simplifying b = -1.5Subproblem 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 = {-1.5, 2}
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