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Simplifying (6s + 8nx2)(s + -1nx2) = 0 Reorder the terms: (8nx2 + 6s)(s + -1nx2) = 0 Reorder the terms: (8nx2 + 6s)(-1nx2 + s) = 0 Multiply (8nx2 + 6s) * (-1nx2 + s) (8nx2 * (-1nx2 + s) + 6s * (-1nx2 + s)) = 0 ((-1nx2 * 8nx2 + s * 8nx2) + 6s * (-1nx2 + s)) = 0 Reorder the terms: ((8nsx2 + -8n2x4) + 6s * (-1nx2 + s)) = 0 ((8nsx2 + -8n2x4) + 6s * (-1nx2 + s)) = 0 (8nsx2 + -8n2x4 + (-1nx2 * 6s + s * 6s)) = 0 (8nsx2 + -8n2x4 + (-6nsx2 + 6s2)) = 0 Reorder the terms: (8nsx2 + -6nsx2 + -8n2x4 + 6s2) = 0 Combine like terms: 8nsx2 + -6nsx2 = 2nsx2 (2nsx2 + -8n2x4 + 6s2) = 0 Solving 2nsx2 + -8n2x4 + 6s2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '2'. 2(nsx2 + -4n2x4 + 3s2) = 0 Factor a trinomial. 2((-4nx2 + -3s)(nx2 + -1s)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4nx2 + -3s)' equal to zero and attempt to solve: Simplifying -4nx2 + -3s = 0 Solving -4nx2 + -3s = 0 Move all terms containing n to the left, all other terms to the right. Add '3s' to each side of the equation. -4nx2 + -3s + 3s = 0 + 3s Combine like terms: -3s + 3s = 0 -4nx2 + 0 = 0 + 3s -4nx2 = 0 + 3s Remove the zero: -4nx2 = 3s Divide each side by '-4x2'. n = -0.75sx-2 Simplifying n = -0.75sx-2Subproblem 2
Set the factor '(nx2 + -1s)' equal to zero and attempt to solve: Simplifying nx2 + -1s = 0 Solving nx2 + -1s = 0 Move all terms containing n to the left, all other terms to the right. Add 's' to each side of the equation. nx2 + -1s + s = 0 + s Combine like terms: -1s + s = 0 nx2 + 0 = 0 + s nx2 = 0 + s Remove the zero: nx2 = s Divide each side by 'x2'. n = sx-2 Simplifying n = sx-2Solution
n = {-0.75sx-2, sx-2}
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