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Simplifying 6b2 + 17b + 7 = -5 Reorder the terms: 7 + 17b + 6b2 = -5 Solving 7 + 17b + 6b2 = -5 Solving for variable 'b'. Reorder the terms: 7 + 5 + 17b + 6b2 = -5 + 5 Combine like terms: 7 + 5 = 12 12 + 17b + 6b2 = -5 + 5 Combine like terms: -5 + 5 = 0 12 + 17b + 6b2 = 0 Factor a trinomial. (3 + 2b)(4 + 3b) = 0Subproblem 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 '(4 + 3b)' equal to zero and attempt to solve: Simplifying 4 + 3b = 0 Solving 4 + 3b = 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 + 3b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3b = 0 + -4 3b = 0 + -4 Combine like terms: 0 + -4 = -4 3b = -4 Divide each side by '3'. b = -1.333333333 Simplifying b = -1.333333333Solution
b = {-1.5, -1.333333333}
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