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Simplifying (2b + -3)(b + -7) = 0 Reorder the terms: (-3 + 2b)(b + -7) = 0 Reorder the terms: (-3 + 2b)(-7 + b) = 0 Multiply (-3 + 2b) * (-7 + b) (-3(-7 + b) + 2b * (-7 + b)) = 0 ((-7 * -3 + b * -3) + 2b * (-7 + b)) = 0 ((21 + -3b) + 2b * (-7 + b)) = 0 (21 + -3b + (-7 * 2b + b * 2b)) = 0 (21 + -3b + (-14b + 2b2)) = 0 Combine like terms: -3b + -14b = -17b (21 + -17b + 2b2) = 0 Solving 21 + -17b + 2b2 = 0 Solving for variable 'b'. Factor a trinomial. (3 + -2b)(7 + -1b) = 0Subproblem 1
Set the factor '(3 + -2b)' equal to zero and attempt to solve: Simplifying 3 + -2b = 0 Solving 3 + -2b = 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 + -2b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2b = 0 + -3 -2b = 0 + -3 Combine like terms: 0 + -3 = -3 -2b = -3 Divide each side by '-2'. b = 1.5 Simplifying b = 1.5Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve: Simplifying 7 + -1b = 0 Solving 7 + -1b = 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 + -1b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1b = 0 + -7 -1b = 0 + -7 Combine like terms: 0 + -7 = -7 -1b = -7 Divide each side by '-1'. b = 7 Simplifying b = 7Solution
b = {1.5, 7}
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