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Simplifying (4b + -3)(3b + -5) = 0 Reorder the terms: (-3 + 4b)(3b + -5) = 0 Reorder the terms: (-3 + 4b)(-5 + 3b) = 0 Multiply (-3 + 4b) * (-5 + 3b) (-3(-5 + 3b) + 4b * (-5 + 3b)) = 0 ((-5 * -3 + 3b * -3) + 4b * (-5 + 3b)) = 0 ((15 + -9b) + 4b * (-5 + 3b)) = 0 (15 + -9b + (-5 * 4b + 3b * 4b)) = 0 (15 + -9b + (-20b + 12b2)) = 0 Combine like terms: -9b + -20b = -29b (15 + -29b + 12b2) = 0 Solving 15 + -29b + 12b2 = 0 Solving for variable 'b'. Factor a trinomial. (3 + -4b)(5 + -3b) = 0Subproblem 1
Set the factor '(3 + -4b)' equal to zero and attempt to solve: Simplifying 3 + -4b = 0 Solving 3 + -4b = 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 + -4b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4b = 0 + -3 -4b = 0 + -3 Combine like terms: 0 + -3 = -3 -4b = -3 Divide each side by '-4'. b = 0.75 Simplifying b = 0.75Subproblem 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 = {0.75, 1.666666667}
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