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Simplifying (2b + -9)(5b + 7) = 0 Reorder the terms: (-9 + 2b)(5b + 7) = 0 Reorder the terms: (-9 + 2b)(7 + 5b) = 0 Multiply (-9 + 2b) * (7 + 5b) (-9(7 + 5b) + 2b * (7 + 5b)) = 0 ((7 * -9 + 5b * -9) + 2b * (7 + 5b)) = 0 ((-63 + -45b) + 2b * (7 + 5b)) = 0 (-63 + -45b + (7 * 2b + 5b * 2b)) = 0 (-63 + -45b + (14b + 10b2)) = 0 Combine like terms: -45b + 14b = -31b (-63 + -31b + 10b2) = 0 Solving -63 + -31b + 10b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -5b)(9 + -2b) = 0Subproblem 1
Set the factor '(-7 + -5b)' equal to zero and attempt to solve: Simplifying -7 + -5b = 0 Solving -7 + -5b = 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 + -5b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5b = 0 + 7 -5b = 0 + 7 Combine like terms: 0 + 7 = 7 -5b = 7 Divide each side by '-5'. b = -1.4 Simplifying b = -1.4Subproblem 2
Set the factor '(9 + -2b)' equal to zero and attempt to solve: Simplifying 9 + -2b = 0 Solving 9 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2b = 0 + -9 -2b = 0 + -9 Combine like terms: 0 + -9 = -9 -2b = -9 Divide each side by '-2'. b = 4.5 Simplifying b = 4.5Solution
b = {-1.4, 4.5}
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