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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. (-3 + -4b)(7 + -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 '(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 = 2.333333333Solution
b = {-0.75, 2.333333333}
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