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Simplifying (3b + -5)(4b + 7) = 0 Reorder the terms: (-5 + 3b)(4b + 7) = 0 Reorder the terms: (-5 + 3b)(7 + 4b) = 0 Multiply (-5 + 3b) * (7 + 4b) (-5(7 + 4b) + 3b * (7 + 4b)) = 0 ((7 * -5 + 4b * -5) + 3b * (7 + 4b)) = 0 ((-35 + -20b) + 3b * (7 + 4b)) = 0 (-35 + -20b + (7 * 3b + 4b * 3b)) = 0 (-35 + -20b + (21b + 12b2)) = 0 Combine like terms: -20b + 21b = 1b (-35 + 1b + 12b2) = 0 Solving -35 + 1b + 12b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -4b)(5 + -3b) = 0Subproblem 1
Set the factor '(-7 + -4b)' equal to zero and attempt to solve: Simplifying -7 + -4b = 0 Solving -7 + -4b = 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 + -4b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4b = 0 + 7 -4b = 0 + 7 Combine like terms: 0 + 7 = 7 -4b = 7 Divide each side by '-4'. b = -1.75 Simplifying b = -1.75Subproblem 2
Set the factor '(5 + -3b)' equal to zero and attempt to solve: Simplifying 5 + -3b = 0 Solving 5 + -3b = 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 + -3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3b = 0 + -5 -3b = 0 + -5 Combine like terms: 0 + -5 = -5 -3b = -5 Divide each side by '-3'. b = 1.666666667 Simplifying b = 1.666666667Solution
b = {-1.75, 1.666666667}
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