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Simplifying 12b2 + 28b + 3 = -12 Reorder the terms: 3 + 28b + 12b2 = -12 Solving 3 + 28b + 12b2 = -12 Solving for variable 'b'. Reorder the terms: 3 + 12 + 28b + 12b2 = -12 + 12 Combine like terms: 3 + 12 = 15 15 + 28b + 12b2 = -12 + 12 Combine like terms: -12 + 12 = 0 15 + 28b + 12b2 = 0 Factor a trinomial. (3 + 2b)(5 + 6b) = 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 '(5 + 6b)' equal to zero and attempt to solve: Simplifying 5 + 6b = 0 Solving 5 + 6b = 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 + 6b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6b = 0 + -5 6b = 0 + -5 Combine like terms: 0 + -5 = -5 6b = -5 Divide each side by '6'. b = -0.8333333333 Simplifying b = -0.8333333333Solution
b = {-1.5, -0.8333333333}
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