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Simplifying 14b2 + 7b + -42 = 0 Reorder the terms: -42 + 7b + 14b2 = 0 Solving -42 + 7b + 14b2 = 0 Solving for variable 'b'. Factor out the Greatest Common Factor (GCF), '7'. 7(-6 + b + 2b2) = 0 Factor a trinomial. 7((-2 + -1b)(3 + -2b)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-2 + -1b)' equal to zero and attempt to solve: Simplifying -2 + -1b = 0 Solving -2 + -1b = 0 Move all terms containing b to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1b = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1b = 0 + 2 -1b = 0 + 2 Combine like terms: 0 + 2 = 2 -1b = 2 Divide each side by '-1'. b = -2 Simplifying b = -2Subproblem 2
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 = 1.5Solution
b = {-2, 1.5}
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