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Simplifying -4b(2b + 5) + 3(b + 7) = 0 Reorder the terms: -4b(5 + 2b) + 3(b + 7) = 0 (5 * -4b + 2b * -4b) + 3(b + 7) = 0 (-20b + -8b2) + 3(b + 7) = 0 Reorder the terms: -20b + -8b2 + 3(7 + b) = 0 -20b + -8b2 + (7 * 3 + b * 3) = 0 -20b + -8b2 + (21 + 3b) = 0 Reorder the terms: 21 + -20b + 3b + -8b2 = 0 Combine like terms: -20b + 3b = -17b 21 + -17b + -8b2 = 0 Solving 21 + -17b + -8b2 = 0 Solving for variable 'b'. Factor a trinomial. (7 + -8b)(3 + b) = 0Subproblem 1
Set the factor '(7 + -8b)' equal to zero and attempt to solve: Simplifying 7 + -8b = 0 Solving 7 + -8b = 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 + -8b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8b = 0 + -7 -8b = 0 + -7 Combine like terms: 0 + -7 = -7 -8b = -7 Divide each side by '-8'. b = 0.875 Simplifying b = 0.875Subproblem 2
Set the factor '(3 + b)' equal to zero and attempt to solve: Simplifying 3 + b = 0 Solving 3 + b = 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 + b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + b = 0 + -3 b = 0 + -3 Combine like terms: 0 + -3 = -3 b = -3 Simplifying b = -3Solution
b = {0.875, -3}
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