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Simplifying (2b + 5)(5b + -3) = 0 Reorder the terms: (5 + 2b)(5b + -3) = 0 Reorder the terms: (5 + 2b)(-3 + 5b) = 0 Multiply (5 + 2b) * (-3 + 5b) (5(-3 + 5b) + 2b * (-3 + 5b)) = 0 ((-3 * 5 + 5b * 5) + 2b * (-3 + 5b)) = 0 ((-15 + 25b) + 2b * (-3 + 5b)) = 0 (-15 + 25b + (-3 * 2b + 5b * 2b)) = 0 (-15 + 25b + (-6b + 10b2)) = 0 Combine like terms: 25b + -6b = 19b (-15 + 19b + 10b2) = 0 Solving -15 + 19b + 10b2 = 0 Solving for variable 'b'. Factor a trinomial. (-5 + -2b)(3 + -5b) = 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 '(3 + -5b)' equal to zero and attempt to solve: Simplifying 3 + -5b = 0 Solving 3 + -5b = 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 + -5b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5b = 0 + -3 -5b = 0 + -3 Combine like terms: 0 + -3 = -3 -5b = -3 Divide each side by '-5'. b = 0.6 Simplifying b = 0.6Solution
b = {-2.5, 0.6}
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