(t^2+vn)(7t^2-6vn)=

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Solution for (t^2+vn)(7t^2-6vn)= equation: 


Simplifying
(t2 + vn)(7t2 + -6vn) = 0

Reorder the terms:
(nv + t2)(7t2 + -6vn) = 0

Reorder the terms:
(nv + t2)(-6nv + 7t2) = 0

Multiply (nv + t2) * (-6nv + 7t2)
(nv(-6nv + 7t2) + t2(-6nv + 7t2)) = 0
((-6nv * nv + 7t2 * nv) + t2(-6nv + 7t2)) = 0

Reorder the terms:
((7nt2v + -6n2v2) + t2(-6nv + 7t2)) = 0
((7nt2v + -6n2v2) + t2(-6nv + 7t2)) = 0
(7nt2v + -6n2v2 + (-6nv * t2 + 7t2 * t2)) = 0
(7nt2v + -6n2v2 + (-6nt2v + 7t4)) = 0

Reorder the terms:
(7nt2v + -6nt2v + -6n2v2 + 7t4) = 0

Combine like terms: 7nt2v + -6nt2v = 1nt2v
(1nt2v + -6n2v2 + 7t4) = 0

Solving
1nt2v + -6n2v2 + 7t4 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1nv + -1t2)(6nv + -7t2) = 0


Subproblem 1
Set the factor '(-1nv + -1t2)' equal to zero and attempt to solve:

Simplifying
-1nv + -1t2 = 0

Solving
-1nv + -1t2 = 0

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

Add 't2' to each side of the equation.
-1nv + -1t2 + t2 = 0 + t2

Combine like terms: -1t2 + t2 = 0
-1nv + 0 = 0 + t2
-1nv = 0 + t2
Remove the zero:
-1nv = t2

Divide each side by '-1v'.
n = -1t2v-1

Simplifying
n = -1t2v-1

Subproblem 2
Set the factor '(6nv + -7t2)' equal to zero and attempt to solve:

Simplifying
6nv + -7t2 = 0

Solving
6nv + -7t2 = 0

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

Add '7t2' to each side of the equation.
6nv + -7t2 + 7t2 = 0 + 7t2

Combine like terms: -7t2 + 7t2 = 0
6nv + 0 = 0 + 7t2
6nv = 0 + 7t2
Remove the zero:
6nv = 7t2

Divide each side by '6v'.
n = 1.166666667t2v-1

Simplifying
n = 1.166666667t2v-1
Solution
n = {-1t2v-1, 1.166666667t2v-1}

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