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Simplifying 10b * b = 27b + -18 Multiply b * b 10b2 = 27b + -18 Reorder the terms: 10b2 = -18 + 27b Solving 10b2 = -18 + 27b Solving for variable 'b'. Reorder the terms: 18 + -27b + 10b2 = -18 + 27b + 18 + -27b Reorder the terms: 18 + -27b + 10b2 = -18 + 18 + 27b + -27b Combine like terms: -18 + 18 = 0 18 + -27b + 10b2 = 0 + 27b + -27b 18 + -27b + 10b2 = 27b + -27b Combine like terms: 27b + -27b = 0 18 + -27b + 10b2 = 0 Factor a trinomial. (6 + -5b)(3 + -2b) = 0Subproblem 1
Set the factor '(6 + -5b)' equal to zero and attempt to solve: Simplifying 6 + -5b = 0 Solving 6 + -5b = 0 Move all terms containing b to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5b = 0 + -6 -5b = 0 + -6 Combine like terms: 0 + -6 = -6 -5b = -6 Divide each side by '-5'. b = 1.2 Simplifying b = 1.2Subproblem 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 = {1.2, 1.5}
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