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Simplifying (3b + 1)(2b + -7) = 0 Reorder the terms: (1 + 3b)(2b + -7) = 0 Reorder the terms: (1 + 3b)(-7 + 2b) = 0 Multiply (1 + 3b) * (-7 + 2b) (1(-7 + 2b) + 3b * (-7 + 2b)) = 0 ((-7 * 1 + 2b * 1) + 3b * (-7 + 2b)) = 0 ((-7 + 2b) + 3b * (-7 + 2b)) = 0 (-7 + 2b + (-7 * 3b + 2b * 3b)) = 0 (-7 + 2b + (-21b + 6b2)) = 0 Combine like terms: 2b + -21b = -19b (-7 + -19b + 6b2) = 0 Solving -7 + -19b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (-1 + -3b)(7 + -2b) = 0Subproblem 1
Set the factor '(-1 + -3b)' equal to zero and attempt to solve: Simplifying -1 + -3b = 0 Solving -1 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3b = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3b = 0 + 1 -3b = 0 + 1 Combine like terms: 0 + 1 = 1 -3b = 1 Divide each side by '-3'. b = -0.3333333333 Simplifying b = -0.3333333333Subproblem 2
Set the factor '(7 + -2b)' equal to zero and attempt to solve: Simplifying 7 + -2b = 0 Solving 7 + -2b = 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 + -2b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2b = 0 + -7 -2b = 0 + -7 Combine like terms: 0 + -7 = -7 -2b = -7 Divide each side by '-2'. b = 3.5 Simplifying b = 3.5Solution
b = {-0.3333333333, 3.5}
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