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Simplifying (b + 3)(6b + -1) = 0 Reorder the terms: (3 + b)(6b + -1) = 0 Reorder the terms: (3 + b)(-1 + 6b) = 0 Multiply (3 + b) * (-1 + 6b) (3(-1 + 6b) + b(-1 + 6b)) = 0 ((-1 * 3 + 6b * 3) + b(-1 + 6b)) = 0 ((-3 + 18b) + b(-1 + 6b)) = 0 (-3 + 18b + (-1 * b + 6b * b)) = 0 (-3 + 18b + (-1b + 6b2)) = 0 Combine like terms: 18b + -1b = 17b (-3 + 17b + 6b2) = 0 Solving -3 + 17b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (-3 + -1b)(1 + -6b) = 0Subproblem 1
Set the factor '(-3 + -1b)' equal to zero and attempt to solve: Simplifying -3 + -1b = 0 Solving -3 + -1b = 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 + -1b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1b = 0 + 3 -1b = 0 + 3 Combine like terms: 0 + 3 = 3 -1b = 3 Divide each side by '-1'. b = -3 Simplifying b = -3Subproblem 2
Set the factor '(1 + -6b)' equal to zero and attempt to solve: Simplifying 1 + -6b = 0 Solving 1 + -6b = 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 + -6b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6b = 0 + -1 -6b = 0 + -1 Combine like terms: 0 + -1 = -1 -6b = -1 Divide each side by '-6'. b = 0.1666666667 Simplifying b = 0.1666666667Solution
b = {-3, 0.1666666667}
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