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Simplifying (5b + 3)(2b + -6) = 0 Reorder the terms: (3 + 5b)(2b + -6) = 0 Reorder the terms: (3 + 5b)(-6 + 2b) = 0 Multiply (3 + 5b) * (-6 + 2b) (3(-6 + 2b) + 5b * (-6 + 2b)) = 0 ((-6 * 3 + 2b * 3) + 5b * (-6 + 2b)) = 0 ((-18 + 6b) + 5b * (-6 + 2b)) = 0 (-18 + 6b + (-6 * 5b + 2b * 5b)) = 0 (-18 + 6b + (-30b + 10b2)) = 0 Combine like terms: 6b + -30b = -24b (-18 + -24b + 10b2) = 0 Solving -18 + -24b + 10b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + -12b + 5b2) = 0 Factor a trinomial. 2((-3 + -5b)(3 + -1b)) = 0 Ignore the factor 2.Subproblem 1
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 = -0.6Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve: Simplifying 3 + -1b = 0 Solving 3 + -1b = 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 + -1b = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1b = 0 + -3 -1b = 0 + -3 Combine like terms: 0 + -3 = -3 -1b = -3 Divide each side by '-1'. b = 3 Simplifying b = 3Solution
b = {-0.6, 3}
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