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Simplifying (b + 3)(b + -7) = 0 Reorder the terms: (3 + b)(b + -7) = 0 Reorder the terms: (3 + b)(-7 + b) = 0 Multiply (3 + b) * (-7 + b) (3(-7 + b) + b(-7 + b)) = 0 ((-7 * 3 + b * 3) + b(-7 + b)) = 0 ((-21 + 3b) + b(-7 + b)) = 0 (-21 + 3b + (-7 * b + b * b)) = 0 (-21 + 3b + (-7b + b2)) = 0 Combine like terms: 3b + -7b = -4b (-21 + -4b + b2) = 0 Solving -21 + -4b + b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -1b)(7 + -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 '(7 + -1b)' equal to zero and attempt to solve: Simplifying 7 + -1b = 0 Solving 7 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1b = 0 + -7 -1b = 0 + -7 Combine like terms: 0 + -7 = -7 -1b = -7 Divide each side by '-1'. b = 7 Simplifying b = 7Solution
b = {-3, 7}
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