2n(n+4)+18=n(n+5)+n(n-2)-7

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Solution for 2n(n+4)+18=n(n+5)+n(n-2)-7 equation: 


Simplifying
2n(n + 4) + 18 = n(n + 5) + n(n + -2) + -7

Reorder the terms:
2n(4 + n) + 18 = n(n + 5) + n(n + -2) + -7
(4 * 2n + n * 2n) + 18 = n(n + 5) + n(n + -2) + -7
(8n + 2n2) + 18 = n(n + 5) + n(n + -2) + -7

Reorder the terms:
18 + 8n + 2n2 = n(n + 5) + n(n + -2) + -7

Reorder the terms:
18 + 8n + 2n2 = n(5 + n) + n(n + -2) + -7
18 + 8n + 2n2 = (5 * n + n * n) + n(n + -2) + -7
18 + 8n + 2n2 = (5n + n2) + n(n + -2) + -7

Reorder the terms:
18 + 8n + 2n2 = 5n + n2 + n(-2 + n) + -7
18 + 8n + 2n2 = 5n + n2 + (-2 * n + n * n) + -7
18 + 8n + 2n2 = 5n + n2 + (-2n + n2) + -7

Reorder the terms:
18 + 8n + 2n2 = -7 + 5n + -2n + n2 + n2

Combine like terms: 5n + -2n = 3n
18 + 8n + 2n2 = -7 + 3n + n2 + n2

Combine like terms: n2 + n2 = 2n2
18 + 8n + 2n2 = -7 + 3n + 2n2

Add '-2n2' to each side of the equation.
18 + 8n + 2n2 + -2n2 = -7 + 3n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
18 + 8n + 0 = -7 + 3n + 2n2 + -2n2
18 + 8n = -7 + 3n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
18 + 8n = -7 + 3n + 0
18 + 8n = -7 + 3n

Solving
18 + 8n = -7 + 3n

Solving for variable 'n'.

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

Add '-3n' to each side of the equation.
18 + 8n + -3n = -7 + 3n + -3n

Combine like terms: 8n + -3n = 5n
18 + 5n = -7 + 3n + -3n

Combine like terms: 3n + -3n = 0
18 + 5n = -7 + 0
18 + 5n = -7

Add '-18' to each side of the equation.
18 + -18 + 5n = -7 + -18

Combine like terms: 18 + -18 = 0
0 + 5n = -7 + -18
5n = -7 + -18

Combine like terms: -7 + -18 = -25
5n = -25

Divide each side by '5'.
n = -5

Simplifying
n = -5

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