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Simplifying (b + 12)(b + -15) = 0 Reorder the terms: (12 + b)(b + -15) = 0 Reorder the terms: (12 + b)(-15 + b) = 0 Multiply (12 + b) * (-15 + b) (12(-15 + b) + b(-15 + b)) = 0 ((-15 * 12 + b * 12) + b(-15 + b)) = 0 ((-180 + 12b) + b(-15 + b)) = 0 (-180 + 12b + (-15 * b + b * b)) = 0 (-180 + 12b + (-15b + b2)) = 0 Combine like terms: 12b + -15b = -3b (-180 + -3b + b2) = 0 Solving -180 + -3b + b2 = 0 Solving for variable 'b'. Factor a trinomial. (-12 + -1b)(15 + -1b) = 0Subproblem 1
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 = -12Subproblem 2
Set the factor '(15 + -1b)' equal to zero and attempt to solve: Simplifying 15 + -1b = 0 Solving 15 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1b = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1b = 0 + -15 -1b = 0 + -15 Combine like terms: 0 + -15 = -15 -1b = -15 Divide each side by '-1'. b = 15 Simplifying b = 15Solution
b = {-12, 15}
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