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Simplifying (5b + -6)(4b + 7) = 0 Reorder the terms: (-6 + 5b)(4b + 7) = 0 Reorder the terms: (-6 + 5b)(7 + 4b) = 0 Multiply (-6 + 5b) * (7 + 4b) (-6(7 + 4b) + 5b * (7 + 4b)) = 0 ((7 * -6 + 4b * -6) + 5b * (7 + 4b)) = 0 ((-42 + -24b) + 5b * (7 + 4b)) = 0 (-42 + -24b + (7 * 5b + 4b * 5b)) = 0 (-42 + -24b + (35b + 20b2)) = 0 Combine like terms: -24b + 35b = 11b (-42 + 11b + 20b2) = 0 Solving -42 + 11b + 20b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -4b)(6 + -5b) = 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 '(6 + -5b)' equal to zero and attempt to solve: Simplifying 6 + -5b = 0 Solving 6 + -5b = 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 + -5b = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5b = 0 + -6 -5b = 0 + -6 Combine like terms: 0 + -6 = -6 -5b = -6 Divide each side by '-5'. b = 1.2 Simplifying b = 1.2Solution
b = {-1.75, 1.2}
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