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Simplifying (4b + -3)(3b + 7) = 0 Reorder the terms: (-3 + 4b)(3b + 7) = 0 Reorder the terms: (-3 + 4b)(7 + 3b) = 0 Multiply (-3 + 4b) * (7 + 3b) (-3(7 + 3b) + 4b * (7 + 3b)) = 0 ((7 * -3 + 3b * -3) + 4b * (7 + 3b)) = 0 ((-21 + -9b) + 4b * (7 + 3b)) = 0 (-21 + -9b + (7 * 4b + 3b * 4b)) = 0 (-21 + -9b + (28b + 12b2)) = 0 Combine like terms: -9b + 28b = 19b (-21 + 19b + 12b2) = 0 Solving -21 + 19b + 12b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -3b)(3 + -4b) = 0Subproblem 1
Set the factor '(-7 + -3b)' equal to zero and attempt to solve: Simplifying -7 + -3b = 0 Solving -7 + -3b = 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 + -3b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3b = 0 + 7 -3b = 0 + 7 Combine like terms: 0 + 7 = 7 -3b = 7 Divide each side by '-3'. b = -2.333333333 Simplifying b = -2.333333333Subproblem 2
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 = 0.75Solution
b = {-2.333333333, 0.75}
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