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Simplifying (5b + -1)(6b + -7) = 0 Reorder the terms: (-1 + 5b)(6b + -7) = 0 Reorder the terms: (-1 + 5b)(-7 + 6b) = 0 Multiply (-1 + 5b) * (-7 + 6b) (-1(-7 + 6b) + 5b * (-7 + 6b)) = 0 ((-7 * -1 + 6b * -1) + 5b * (-7 + 6b)) = 0 ((7 + -6b) + 5b * (-7 + 6b)) = 0 (7 + -6b + (-7 * 5b + 6b * 5b)) = 0 (7 + -6b + (-35b + 30b2)) = 0 Combine like terms: -6b + -35b = -41b (7 + -41b + 30b2) = 0 Solving 7 + -41b + 30b2 = 0 Solving for variable 'b'. Factor a trinomial. (1 + -5b)(7 + -6b) = 0Subproblem 1
Set the factor '(1 + -5b)' equal to zero and attempt to solve: Simplifying 1 + -5b = 0 Solving 1 + -5b = 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 + -5b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5b = 0 + -1 -5b = 0 + -1 Combine like terms: 0 + -1 = -1 -5b = -1 Divide each side by '-5'. b = 0.2 Simplifying b = 0.2Subproblem 2
Set the factor '(7 + -6b)' equal to zero and attempt to solve: Simplifying 7 + -6b = 0 Solving 7 + -6b = 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 + -6b = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6b = 0 + -7 -6b = 0 + -7 Combine like terms: 0 + -7 = -7 -6b = -7 Divide each side by '-6'. b = 1.166666667 Simplifying b = 1.166666667Solution
b = {0.2, 1.166666667}
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