2n(n+4)+n(n-2)-15=-3n(-n+1)+2n+6

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Solution for 2n(n+4)+n(n-2)-15=-3n(-n+1)+2n+6 equation: 


Simplifying
2n(n + 4) + n(n + -2) + -15 = -3n(-1n + 1) + 2n + 6

Reorder the terms:
2n(4 + n) + n(n + -2) + -15 = -3n(-1n + 1) + 2n + 6
(4 * 2n + n * 2n) + n(n + -2) + -15 = -3n(-1n + 1) + 2n + 6
(8n + 2n2) + n(n + -2) + -15 = -3n(-1n + 1) + 2n + 6

Reorder the terms:
8n + 2n2 + n(-2 + n) + -15 = -3n(-1n + 1) + 2n + 6
8n + 2n2 + (-2 * n + n * n) + -15 = -3n(-1n + 1) + 2n + 6
8n + 2n2 + (-2n + n2) + -15 = -3n(-1n + 1) + 2n + 6

Reorder the terms:
-15 + 8n + -2n + 2n2 + n2 = -3n(-1n + 1) + 2n + 6

Combine like terms: 8n + -2n = 6n
-15 + 6n + 2n2 + n2 = -3n(-1n + 1) + 2n + 6

Combine like terms: 2n2 + n2 = 3n2
-15 + 6n + 3n2 = -3n(-1n + 1) + 2n + 6

Reorder the terms:
-15 + 6n + 3n2 = -3n(1 + -1n) + 2n + 6
-15 + 6n + 3n2 = (1 * -3n + -1n * -3n) + 2n + 6
-15 + 6n + 3n2 = (-3n + 3n2) + 2n + 6

Reorder the terms:
-15 + 6n + 3n2 = 6 + -3n + 2n + 3n2

Combine like terms: -3n + 2n = -1n
-15 + 6n + 3n2 = 6 + -1n + 3n2

Add '-3n2' to each side of the equation.
-15 + 6n + 3n2 + -3n2 = 6 + -1n + 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
-15 + 6n + 0 = 6 + -1n + 3n2 + -3n2
-15 + 6n = 6 + -1n + 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
-15 + 6n = 6 + -1n + 0
-15 + 6n = 6 + -1n

Solving
-15 + 6n = 6 + -1n

Solving for variable 'n'.

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

Add 'n' to each side of the equation.
-15 + 6n + n = 6 + -1n + n

Combine like terms: 6n + n = 7n
-15 + 7n = 6 + -1n + n

Combine like terms: -1n + n = 0
-15 + 7n = 6 + 0
-15 + 7n = 6

Add '15' to each side of the equation.
-15 + 15 + 7n = 6 + 15

Combine like terms: -15 + 15 = 0
0 + 7n = 6 + 15
7n = 6 + 15

Combine like terms: 6 + 15 = 21
7n = 21

Divide each side by '7'.
n = 3

Simplifying
n = 3

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