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Simplifying (6b + 13)(b + 12) = 0 Reorder the terms: (13 + 6b)(b + 12) = 0 Reorder the terms: (13 + 6b)(12 + b) = 0 Multiply (13 + 6b) * (12 + b) (13(12 + b) + 6b * (12 + b)) = 0 ((12 * 13 + b * 13) + 6b * (12 + b)) = 0 ((156 + 13b) + 6b * (12 + b)) = 0 (156 + 13b + (12 * 6b + b * 6b)) = 0 (156 + 13b + (72b + 6b2)) = 0 Combine like terms: 13b + 72b = 85b (156 + 85b + 6b2) = 0 Solving 156 + 85b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (12 + b)(13 + 6b) = 0Subproblem 1
Set the factor '(12 + b)' equal to zero and attempt to solve: Simplifying 12 + b = 0 Solving 12 + b = 0 Move all terms containing b to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + b = 0 + -12 Combine like terms: 12 + -12 = 0 0 + b = 0 + -12 b = 0 + -12 Combine like terms: 0 + -12 = -12 b = -12 Simplifying b = -12Subproblem 2
Set the factor '(13 + 6b)' equal to zero and attempt to solve: Simplifying 13 + 6b = 0 Solving 13 + 6b = 0 Move all terms containing b to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + 6b = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 6b = 0 + -13 6b = 0 + -13 Combine like terms: 0 + -13 = -13 6b = -13 Divide each side by '6'. b = -2.166666667 Simplifying b = -2.166666667Solution
b = {-12, -2.166666667}
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