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Simplifying (b + 3)(b + -6) = 0 Reorder the terms: (3 + b)(b + -6) = 0 Reorder the terms: (3 + b)(-6 + b) = 0 Multiply (3 + b) * (-6 + b) (3(-6 + b) + b(-6 + b)) = 0 ((-6 * 3 + b * 3) + b(-6 + b)) = 0 ((-18 + 3b) + b(-6 + b)) = 0 (-18 + 3b + (-6 * b + b * b)) = 0 (-18 + 3b + (-6b + b2)) = 0 Combine like terms: 3b + -6b = -3b (-18 + -3b + b2) = 0 Solving -18 + -3b + b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -1b)(6 + -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 '(6 + -1b)' equal to zero and attempt to solve: Simplifying 6 + -1b = 0 Solving 6 + -1b = 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 + -1b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1b = 0 + -6 -1b = 0 + -6 Combine like terms: 0 + -6 = -6 -1b = -6 Divide each side by '-1'. b = 6 Simplifying b = 6Solution
b = {-3, 6}
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