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Simplifying (4b + -5)(-3b + 2) = 0 Reorder the terms: (-5 + 4b)(-3b + 2) = 0 Reorder the terms: (-5 + 4b)(2 + -3b) = 0 Multiply (-5 + 4b) * (2 + -3b) (-5(2 + -3b) + 4b * (2 + -3b)) = 0 ((2 * -5 + -3b * -5) + 4b * (2 + -3b)) = 0 ((-10 + 15b) + 4b * (2 + -3b)) = 0 (-10 + 15b + (2 * 4b + -3b * 4b)) = 0 (-10 + 15b + (8b + -12b2)) = 0 Combine like terms: 15b + 8b = 23b (-10 + 23b + -12b2) = 0 Solving -10 + 23b + -12b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + 4b)(2 + -3b) = 0Subproblem 1
Set the factor '(-5 + 4b)' equal to zero and attempt to solve: Simplifying -5 + 4b = 0 Solving -5 + 4b = 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 + 4b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4b = 0 + 5 4b = 0 + 5 Combine like terms: 0 + 5 = 5 4b = 5 Divide each side by '4'. b = 1.25 Simplifying b = 1.25Subproblem 2
Set the factor '(2 + -3b)' equal to zero and attempt to solve: Simplifying 2 + -3b = 0 Solving 2 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3b = 0 + -2 -3b = 0 + -2 Combine like terms: 0 + -2 = -2 -3b = -2 Divide each side by '-3'. b = 0.6666666667 Simplifying b = 0.6666666667Solution
b = {1.25, 0.6666666667}
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