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Simplifying (3b2 + 7b + 5) + (3b2 + -8) = 0 Reorder the terms: (5 + 7b + 3b2) + (3b2 + -8) = 0 Remove parenthesis around (5 + 7b + 3b2) 5 + 7b + 3b2 + (3b2 + -8) = 0 Reorder the terms: 5 + 7b + 3b2 + (-8 + 3b2) = 0 Remove parenthesis around (-8 + 3b2) 5 + 7b + 3b2 + -8 + 3b2 = 0 Reorder the terms: 5 + -8 + 7b + 3b2 + 3b2 = 0 Combine like terms: 5 + -8 = -3 -3 + 7b + 3b2 + 3b2 = 0 Combine like terms: 3b2 + 3b2 = 6b2 -3 + 7b + 6b2 = 0 Solving -3 + 7b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -2b)(1 + -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 '(1 + -3b)' equal to zero and attempt to solve: Simplifying 1 + -3b = 0 Solving 1 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3b = 0 + -1 -3b = 0 + -1 Combine like terms: 0 + -1 = -1 -3b = -1 Divide each side by '-3'. b = 0.3333333333 Simplifying b = 0.3333333333Solution
b = {-1.5, 0.3333333333}
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