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Simplifying (2b + 5)(3b + -2) = 0 Reorder the terms: (5 + 2b)(3b + -2) = 0 Reorder the terms: (5 + 2b)(-2 + 3b) = 0 Multiply (5 + 2b) * (-2 + 3b) (5(-2 + 3b) + 2b * (-2 + 3b)) = 0 ((-2 * 5 + 3b * 5) + 2b * (-2 + 3b)) = 0 ((-10 + 15b) + 2b * (-2 + 3b)) = 0 (-10 + 15b + (-2 * 2b + 3b * 2b)) = 0 (-10 + 15b + (-4b + 6b2)) = 0 Combine like terms: 15b + -4b = 11b (-10 + 11b + 6b2) = 0 Solving -10 + 11b + 6b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -2b)(2 + -3b) = 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 '(2 + -3b)' equal to zero and attempt to solve: Simplifying 2 + -3b = 0 Solving 2 + -3b = 0 Move all terms containing b to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3b = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3b = 0 + -2 -3b = 0 + -2 Combine like terms: 0 + -2 = -2 -3b = -2 Divide each side by '-3'. b = 0.6666666667 Simplifying b = 0.6666666667Solution
b = {-2.5, 0.6666666667}
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