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Simplifying (b(b + 12)) = 189 Reorder the terms: (b(12 + b)) = 189 ((12 * b + b * b)) = 189 ((12b + b2)) = 189 (12b + b2) = 189 Remove parenthesis around (12b + b2) 12b + b2 = 189 Solving 12b + b2 = 189 Solving for variable 'b'. Reorder the terms: -189 + 12b + b2 = 189 + -189 Combine like terms: 189 + -189 = 0 -189 + 12b + b2 = 0 Factor a trinomial. (-21 + -1b)(9 + -1b) = 0Subproblem 1
Set the factor '(-21 + -1b)' equal to zero and attempt to solve: Simplifying -21 + -1b = 0 Solving -21 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -1b = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -1b = 0 + 21 -1b = 0 + 21 Combine like terms: 0 + 21 = 21 -1b = 21 Divide each side by '-1'. b = -21 Simplifying b = -21Subproblem 2
Set the factor '(9 + -1b)' equal to zero and attempt to solve: Simplifying 9 + -1b = 0 Solving 9 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1b = 0 + -9 -1b = 0 + -9 Combine like terms: 0 + -9 = -9 -1b = -9 Divide each side by '-1'. b = 9 Simplifying b = 9Solution
b = {-21, 9}
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