(6s+8nx^2)(s-nx^2)=0

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Solution for (6s+8nx^2)(s-nx^2)=0 equation: 


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-2

Subproblem 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-2
Solution
n = {-0.75sx-2, sx-2}

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