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Simplifying (2b + 5)(6b + -7) = 0 Reorder the terms: (5 + 2b)(6b + -7) = 0 Reorder the terms: (5 + 2b)(-7 + 6b) = 0 Multiply (5 + 2b) * (-7 + 6b) (5(-7 + 6b) + 2b * (-7 + 6b)) = 0 ((-7 * 5 + 6b * 5) + 2b * (-7 + 6b)) = 0 ((-35 + 30b) + 2b * (-7 + 6b)) = 0 (-35 + 30b + (-7 * 2b + 6b * 2b)) = 0 (-35 + 30b + (-14b + 12b2)) = 0 Combine like terms: 30b + -14b = 16b (-35 + 16b + 12b2) = 0 Solving -35 + 16b + 12b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -2b)(7 + -6b) = 0Subproblem 1
Set the factor '(-5 + -2b)' equal to zero and attempt to solve: Simplifying -5 + -2b = 0 Solving -5 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2b = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2b = 0 + 5 -2b = 0 + 5 Combine like terms: 0 + 5 = 5 -2b = 5 Divide each side by '-2'. b = -2.5 Simplifying b = -2.5Subproblem 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 = {-2.5, 1.166666667}
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