(v-4nt)(v+nt)=0

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Solution for (v-4nt)(v+nt)=0 equation: 


Simplifying
(v + -4nt)(v + nt) = 0

Reorder the terms:
(-4nt + v)(v + nt) = 0

Reorder the terms:
(-4nt + v)(nt + v) = 0

Multiply (-4nt + v) * (nt + v)
(-4nt * (nt + v) + v(nt + v)) = 0
((nt * -4nt + v * -4nt) + v(nt + v)) = 0

Reorder the terms:
((-4ntv + -4n2t2) + v(nt + v)) = 0
((-4ntv + -4n2t2) + v(nt + v)) = 0
(-4ntv + -4n2t2 + (nt * v + v * v)) = 0
(-4ntv + -4n2t2 + (ntv + v2)) = 0

Reorder the terms:
(-4ntv + ntv + -4n2t2 + v2) = 0

Combine like terms: -4ntv + ntv = -3ntv
(-3ntv + -4n2t2 + v2) = 0

Solving
-3ntv + -4n2t2 + v2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1nt + -1v)(4nt + -1v) = 0


Subproblem 1
Set the factor '(-1nt + -1v)' equal to zero and attempt to solve:

Simplifying
-1nt + -1v = 0

Solving
-1nt + -1v = 0

Move all terms containing n to the left, all other terms to the right.

Add 'v' to each side of the equation.
-1nt + -1v + v = 0 + v

Combine like terms: -1v + v = 0
-1nt + 0 = 0 + v
-1nt = 0 + v
Remove the zero:
-1nt = v

Divide each side by '-1t'.
n = -1t-1v

Simplifying
n = -1t-1v

Subproblem 2
Set the factor '(4nt + -1v)' equal to zero and attempt to solve:

Simplifying
4nt + -1v = 0

Solving
4nt + -1v = 0

Move all terms containing n to the left, all other terms to the right.

Add 'v' to each side of the equation.
4nt + -1v + v = 0 + v

Combine like terms: -1v + v = 0
4nt + 0 = 0 + v
4nt = 0 + v
Remove the zero:
4nt = v

Divide each side by '4t'.
n = 0.25t-1v

Simplifying
n = 0.25t-1v
Solution
n = {-1t-1v, 0.25t-1v}

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