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Simplifying -3b(4b + -10) = 0.5(-24 + 60) Reorder the terms: -3b(-10 + 4b) = 0.5(-24 + 60) (-10 * -3b + 4b * -3b) = 0.5(-24 + 60) (30b + -12b2) = 0.5(-24 + 60) Combine like terms: -24 + 60 = 36 30b + -12b2 = 0.5(36) Multiply 0.5 * 36 30b + -12b2 = 18 Solving 30b + -12b2 = 18 Solving for variable 'b'. Reorder the terms: -18 + 30b + -12b2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 30b + -12b2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 5b + -2b2) = 0 Factor a trinomial. 6((-3 + 2b)(1 + -1b)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + 2b)' equal to zero and attempt to solve: Simplifying -3 + 2b = 0 Solving -3 + 2b = 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 + 2b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2b = 0 + 3 2b = 0 + 3 Combine like terms: 0 + 3 = 3 2b = 3 Divide each side by '2'. b = 1.5 Simplifying b = 1.5Subproblem 2
Set the factor '(1 + -1b)' equal to zero and attempt to solve: Simplifying 1 + -1b = 0 Solving 1 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1b = 0 + -1 -1b = 0 + -1 Combine like terms: 0 + -1 = -1 -1b = -1 Divide each side by '-1'. b = 1 Simplifying b = 1Solution
b = {1.5, 1}
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