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Simplifying (b + 3)(b + -12) = 0 Reorder the terms: (3 + b)(b + -12) = 0 Reorder the terms: (3 + b)(-12 + b) = 0 Multiply (3 + b) * (-12 + b) (3(-12 + b) + b(-12 + b)) = 0 ((-12 * 3 + b * 3) + b(-12 + b)) = 0 ((-36 + 3b) + b(-12 + b)) = 0 (-36 + 3b + (-12 * b + b * b)) = 0 (-36 + 3b + (-12b + b2)) = 0 Combine like terms: 3b + -12b = -9b (-36 + -9b + b2) = 0 Solving -36 + -9b + b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -1b)(12 + -1b) = 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 '(12 + -1b)' equal to zero and attempt to solve: Simplifying 12 + -1b = 0 Solving 12 + -1b = 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 + -1b = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1b = 0 + -12 -1b = 0 + -12 Combine like terms: 0 + -12 = -12 -1b = -12 Divide each side by '-1'. b = 12 Simplifying b = 12Solution
b = {-3, 12}
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