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Simplifying (b + -1vn)(b + -7vn) = 0 Multiply (b + -1nv) * (b + -7nv) (b(b + -7nv) + -1nv * (b + -7nv)) = 0 ((b * b + -7nv * b) + -1nv * (b + -7nv)) = 0 Reorder the terms: ((-7bnv + b2) + -1nv * (b + -7nv)) = 0 ((-7bnv + b2) + -1nv * (b + -7nv)) = 0 (-7bnv + b2 + (b * -1nv + -7nv * -1nv)) = 0 (-7bnv + b2 + (-1bnv + 7n2v2)) = 0 Reorder the terms: (-7bnv + -1bnv + b2 + 7n2v2) = 0 Combine like terms: -7bnv + -1bnv = -8bnv (-8bnv + b2 + 7n2v2) = 0 Solving -8bnv + b2 + 7n2v2 = 0 Solving for variable 'b'. Factor a trinomial. (b + -7nv)(b + -1nv) = 0Subproblem 1
Set the factor '(b + -7nv)' equal to zero and attempt to solve: Simplifying b + -7nv = 0 Solving b + -7nv = 0 Move all terms containing b to the left, all other terms to the right. Add '7nv' to each side of the equation. b + -7nv + 7nv = 0 + 7nv Combine like terms: -7nv + 7nv = 0 b + 0 = 0 + 7nv b = 0 + 7nv Remove the zero: b = 7nv Simplifying b = 7nvSubproblem 2
Set the factor '(b + -1nv)' equal to zero and attempt to solve: Simplifying b + -1nv = 0 Solving b + -1nv = 0 Move all terms containing b to the left, all other terms to the right. Add 'nv' to each side of the equation. b + -1nv + nv = 0 + nv Combine like terms: -1nv + nv = 0 b + 0 = 0 + nv b = 0 + nv Remove the zero: b = nv Simplifying b = nvSolution
b = {7nv, nv}
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