0=n^2-6np+8p^2

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Solution for 0=n^2-6np+8p^2 equation: 


Simplifying
0 = n2 + -6np + 8p2

Reorder the terms:
0 = -6np + n2 + 8p2

Solving
0 = -6np + n2 + 8p2

Solving for variable 'n'.
Remove the zero:
6np + -1n2 + -8p2 = -6np + n2 + 8p2 + 6np + -1n2 + -8p2

Reorder the terms:
6np + -1n2 + -8p2 = -6np + 6np + n2 + -1n2 + 8p2 + -8p2

Combine like terms: -6np + 6np = 0
6np + -1n2 + -8p2 = 0 + n2 + -1n2 + 8p2 + -8p2
6np + -1n2 + -8p2 = n2 + -1n2 + 8p2 + -8p2

Combine like terms: n2 + -1n2 = 0
6np + -1n2 + -8p2 = 0 + 8p2 + -8p2
6np + -1n2 + -8p2 = 8p2 + -8p2

Combine like terms: 8p2 + -8p2 = 0
6np + -1n2 + -8p2 = 0

Factor a trinomial.
(-1n + 2p)(n + -4p) = 0


Subproblem 1
Set the factor '(-1n + 2p)' equal to zero and attempt to solve:

Simplifying
-1n + 2p = 0

Solving
-1n + 2p = 0

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

Add '-2p' to each side of the equation.
-1n + 2p + -2p = 0 + -2p

Combine like terms: 2p + -2p = 0
-1n + 0 = 0 + -2p
-1n = 0 + -2p
Remove the zero:
-1n = -2p

Divide each side by '-1'.
n = 2p

Simplifying
n = 2p

Subproblem 2
Set the factor '(n + -4p)' equal to zero and attempt to solve:

Simplifying
n + -4p = 0

Solving
n + -4p = 0

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

Add '4p' to each side of the equation.
n + -4p + 4p = 0 + 4p

Combine like terms: -4p + 4p = 0
n + 0 = 0 + 4p
n = 0 + 4p
Remove the zero:
n = 4p

Simplifying
n = 4p
Solution
n = {2p, 4p}

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