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Simplifying (3b + -4)(4b + -3) = 0 Reorder the terms: (-4 + 3b)(4b + -3) = 0 Reorder the terms: (-4 + 3b)(-3 + 4b) = 0 Multiply (-4 + 3b) * (-3 + 4b) (-4(-3 + 4b) + 3b * (-3 + 4b)) = 0 ((-3 * -4 + 4b * -4) + 3b * (-3 + 4b)) = 0 ((12 + -16b) + 3b * (-3 + 4b)) = 0 (12 + -16b + (-3 * 3b + 4b * 3b)) = 0 (12 + -16b + (-9b + 12b2)) = 0 Combine like terms: -16b + -9b = -25b (12 + -25b + 12b2) = 0 Solving 12 + -25b + 12b2 = 0 Solving for variable 'b'. Factor a trinomial. (3 + -4b)(4 + -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 '(4 + -3b)' equal to zero and attempt to solve: Simplifying 4 + -3b = 0 Solving 4 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3b = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3b = 0 + -4 -3b = 0 + -4 Combine like terms: 0 + -4 = -4 -3b = -4 Divide each side by '-3'. b = 1.333333333 Simplifying b = 1.333333333Solution
b = {0.75, 1.333333333}
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