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Simplifying 30b3 + 145b2 + -210b = 0 Reorder the terms: -210b + 145b2 + 30b3 = 0 Solving -210b + 145b2 + 30b3 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '5b'. 5b(-42 + 29b + 6b2) = 0 Factor a trinomial. 5b((-6 + -1b)(7 + -6b)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'b' equal to zero and attempt to solve: Simplifying b = 0 Solving b = 0 Move all terms containing b to the left, all other terms to the right. Simplifying b = 0Subproblem 2
Set the factor '(-6 + -1b)' equal to zero and attempt to solve: Simplifying -6 + -1b = 0 Solving -6 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1b = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1b = 0 + 6 -1b = 0 + 6 Combine like terms: 0 + 6 = 6 -1b = 6 Divide each side by '-1'. b = -6 Simplifying b = -6Subproblem 3
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 = 1.166666667Solution
b = {0, -6, 1.166666667}
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