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Simplifying (y + nv)(4y + 4nv) = 0 Reorder the terms: (nv + y)(4y + 4nv) = 0 Reorder the terms: (nv + y)(4nv + 4y) = 0 Multiply (nv + y) * (4nv + 4y) (nv(4nv + 4y) + y(4nv + 4y)) = 0 ((4nv * nv + 4y * nv) + y(4nv + 4y)) = 0 Reorder the terms: ((4nvy + 4n2v2) + y(4nv + 4y)) = 0 ((4nvy + 4n2v2) + y(4nv + 4y)) = 0 (4nvy + 4n2v2 + (4nv * y + 4y * y)) = 0 (4nvy + 4n2v2 + (4nvy + 4y2)) = 0 Reorder the terms: (4nvy + 4nvy + 4n2v2 + 4y2) = 0 Combine like terms: 4nvy + 4nvy = 8nvy (8nvy + 4n2v2 + 4y2) = 0 Solving 8nvy + 4n2v2 + 4y2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(2nvy + n2v2 + y2) = 0 Factor a trinomial. 4((nv + y)(nv + y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(nv + y)' equal to zero and attempt to solve: Simplifying nv + y = 0 Solving nv + y = 0 Move all terms containing n to the left, all other terms to the right. Add '-1y' to each side of the equation. nv + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 nv + 0 = 0 + -1y nv = 0 + -1y Remove the zero: nv = -1y Divide each side by 'v'. n = -1v-1y Simplifying n = -1v-1ySubproblem 2
Set the factor '(nv + y)' equal to zero and attempt to solve: Simplifying nv + y = 0 Solving nv + y = 0 Move all terms containing n to the left, all other terms to the right. Add '-1y' to each side of the equation. nv + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 nv + 0 = 0 + -1y nv = 0 + -1y Remove the zero: nv = -1y Divide each side by 'v'. n = -1v-1y Simplifying n = -1v-1ySolution
n = {-1v-1y, -1v-1y}
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