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Simplifying (b + 5)(2b + -7) = 0 Reorder the terms: (5 + b)(2b + -7) = 0 Reorder the terms: (5 + b)(-7 + 2b) = 0 Multiply (5 + b) * (-7 + 2b) (5(-7 + 2b) + b(-7 + 2b)) = 0 ((-7 * 5 + 2b * 5) + b(-7 + 2b)) = 0 ((-35 + 10b) + b(-7 + 2b)) = 0 (-35 + 10b + (-7 * b + 2b * b)) = 0 (-35 + 10b + (-7b + 2b2)) = 0 Combine like terms: 10b + -7b = 3b (-35 + 3b + 2b2) = 0 Solving -35 + 3b + 2b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -1b)(7 + -2b) = 0Subproblem 1
Set the factor '(-5 + -1b)' equal to zero and attempt to solve: Simplifying -5 + -1b = 0 Solving -5 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1b = 0 + 5 -1b = 0 + 5 Combine like terms: 0 + 5 = 5 -1b = 5 Divide each side by '-1'. b = -5 Simplifying b = -5Subproblem 2
Set the factor '(7 + -2b)' equal to zero and attempt to solve: Simplifying 7 + -2b = 0 Solving 7 + -2b = 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 + -2b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2b = 0 + -7 -2b = 0 + -7 Combine like terms: 0 + -7 = -7 -2b = -7 Divide each side by '-2'. b = 3.5 Simplifying b = 3.5Solution
b = {-5, 3.5}
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