n(2n+k)-n-1(2n-1+k)=4n+3

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Solution for n(2n+k)-n-1(2n-1+k)=4n+3 equation: 


Simplifying
n(2n + k) + -1n + -1(2n + -1 + k) = 4n + 3

Reorder the terms:
n(k + 2n) + -1n + -1(2n + -1 + k) = 4n + 3
(k * n + 2n * n) + -1n + -1(2n + -1 + k) = 4n + 3
(kn + 2n2) + -1n + -1(2n + -1 + k) = 4n + 3

Reorder the terms:
kn + 2n2 + -1n + -1(-1 + k + 2n) = 4n + 3
kn + 2n2 + -1n + (-1 * -1 + k * -1 + 2n * -1) = 4n + 3
kn + 2n2 + -1n + (1 + -1k + -2n) = 4n + 3

Reorder the terms:
1 + -1k + kn + -1n + -2n + 2n2 = 4n + 3

Combine like terms: -1n + -2n = -3n
1 + -1k + kn + -3n + 2n2 = 4n + 3

Reorder the terms:
1 + -1k + kn + -3n + 2n2 = 3 + 4n

Solving
1 + -1k + kn + -3n + 2n2 = 3 + 4n

Solving for variable 'k'.

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

Add '-1' to each side of the equation.
1 + -1k + kn + -3n + -1 + 2n2 = 3 + -1 + 4n

Reorder the terms:
1 + -1 + -1k + kn + -3n + 2n2 = 3 + -1 + 4n

Combine like terms: 1 + -1 = 0
0 + -1k + kn + -3n + 2n2 = 3 + -1 + 4n
-1k + kn + -3n + 2n2 = 3 + -1 + 4n

Combine like terms: 3 + -1 = 2
-1k + kn + -3n + 2n2 = 2 + 4n

Add '3n' to each side of the equation.
-1k + kn + -3n + 3n + 2n2 = 2 + 4n + 3n

Combine like terms: -3n + 3n = 0
-1k + kn + 0 + 2n2 = 2 + 4n + 3n
-1k + kn + 2n2 = 2 + 4n + 3n

Combine like terms: 4n + 3n = 7n
-1k + kn + 2n2 = 2 + 7n

Add '-2n2' to each side of the equation.
-1k + kn + 2n2 + -2n2 = 2 + 7n + -2n2

Combine like terms: 2n2 + -2n2 = 0
-1k + kn + 0 = 2 + 7n + -2n2
-1k + kn = 2 + 7n + -2n2

Reorder the terms:
-2 + -1k + kn + -7n + 2n2 = 2 + 7n + -2n2 + -2 + -7n + 2n2

Reorder the terms:
-2 + -1k + kn + -7n + 2n2 = 2 + -2 + 7n + -7n + -2n2 + 2n2

Combine like terms: 2 + -2 = 0
-2 + -1k + kn + -7n + 2n2 = 0 + 7n + -7n + -2n2 + 2n2
-2 + -1k + kn + -7n + 2n2 = 7n + -7n + -2n2 + 2n2

Combine like terms: 7n + -7n = 0
-2 + -1k + kn + -7n + 2n2 = 0 + -2n2 + 2n2
-2 + -1k + kn + -7n + 2n2 = -2n2 + 2n2

Combine like terms: -2n2 + 2n2 = 0
-2 + -1k + kn + -7n + 2n2 = 0

The solution to this equation could not be determined.

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