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Simplifying (6b + 7)(3b + -5) = 0 Reorder the terms: (7 + 6b)(3b + -5) = 0 Reorder the terms: (7 + 6b)(-5 + 3b) = 0 Multiply (7 + 6b) * (-5 + 3b) (7(-5 + 3b) + 6b * (-5 + 3b)) = 0 ((-5 * 7 + 3b * 7) + 6b * (-5 + 3b)) = 0 ((-35 + 21b) + 6b * (-5 + 3b)) = 0 (-35 + 21b + (-5 * 6b + 3b * 6b)) = 0 (-35 + 21b + (-30b + 18b2)) = 0 Combine like terms: 21b + -30b = -9b (-35 + -9b + 18b2) = 0 Solving -35 + -9b + 18b2 = 0 Solving for variable 'b'. Factor a trinomial. (-7 + -6b)(5 + -3b) = 0Subproblem 1
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 = -1.166666667Subproblem 2
Set the factor '(5 + -3b)' equal to zero and attempt to solve: Simplifying 5 + -3b = 0 Solving 5 + -3b = 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 + -3b = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3b = 0 + -5 -3b = 0 + -5 Combine like terms: 0 + -5 = -5 -3b = -5 Divide each side by '-3'. b = 1.666666667 Simplifying b = 1.666666667Solution
b = {-1.166666667, 1.666666667}
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