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Simplifying b(2b + 3) = 9 Reorder the terms: b(3 + 2b) = 9 (3 * b + 2b * b) = 9 (3b + 2b2) = 9 Solving 3b + 2b2 = 9 Solving for variable 'b'. Reorder the terms: -9 + 3b + 2b2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 3b + 2b2 = 0 Factor a trinomial. (-3 + -1b)(3 + -2b) = 0Subproblem 1
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 = -3Subproblem 2
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 = 1.5Solution
b = {-3, 1.5}
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