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Simplifying 20b3 + 50b2 = 70b Reorder the terms: 50b2 + 20b3 = 70b Solving 50b2 + 20b3 = 70b Solving for variable 'b'. Reorder the terms: -70b + 50b2 + 20b3 = 70b + -70b Combine like terms: 70b + -70b = 0 -70b + 50b2 + 20b3 = 0 Factor out the Greatest Common Factor (GCF), '10b'. 10b(-7 + 5b + 2b2) = 0 Factor a trinomial. 10b((-7 + -2b)(1 + -1b)) = 0 Ignore the factor 10.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 '(-7 + -2b)' equal to zero and attempt to solve: Simplifying -7 + -2b = 0 Solving -7 + -2b = 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 + -2b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2b = 0 + 7 -2b = 0 + 7 Combine like terms: 0 + 7 = 7 -2b = 7 Divide each side by '-2'. b = -3.5 Simplifying b = -3.5Subproblem 3
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 = {0, -3.5, 1}
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