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Simplifying 4b2 + -32b + -420 = 0 Reorder the terms: -420 + -32b + 4b2 = 0 Solving -420 + -32b + 4b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '4'. 4(-105 + -8b + b2) = 0 Factor a trinomial. 4((-7 + -1b)(15 + -1b)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -1b)' equal to zero and attempt to solve: Simplifying -7 + -1b = 0 Solving -7 + -1b = 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 + -1b = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1b = 0 + 7 -1b = 0 + 7 Combine like terms: 0 + 7 = 7 -1b = 7 Divide each side by '-1'. b = -7 Simplifying b = -7Subproblem 2
Set the factor '(15 + -1b)' equal to zero and attempt to solve: Simplifying 15 + -1b = 0 Solving 15 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1b = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1b = 0 + -15 -1b = 0 + -15 Combine like terms: 0 + -15 = -15 -1b = -15 Divide each side by '-1'. b = 15 Simplifying b = 15Solution
b = {-7, 15}
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