n(n+5)+n(n+2)=n(2n+1)+n-45

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Solution for n(n+5)+n(n+2)=n(2n+1)+n-45 equation: 


Simplifying
n(n + 5) + n(n + 2) = n(2n + 1) + n + -45

Reorder the terms:
n(5 + n) + n(n + 2) = n(2n + 1) + n + -45
(5 * n + n * n) + n(n + 2) = n(2n + 1) + n + -45
(5n + n2) + n(n + 2) = n(2n + 1) + n + -45

Reorder the terms:
5n + n2 + n(2 + n) = n(2n + 1) + n + -45
5n + n2 + (2 * n + n * n) = n(2n + 1) + n + -45
5n + n2 + (2n + n2) = n(2n + 1) + n + -45

Reorder the terms:
5n + 2n + n2 + n2 = n(2n + 1) + n + -45

Combine like terms: 5n + 2n = 7n
7n + n2 + n2 = n(2n + 1) + n + -45

Combine like terms: n2 + n2 = 2n2
7n + 2n2 = n(2n + 1) + n + -45

Reorder the terms:
7n + 2n2 = n(1 + 2n) + n + -45
7n + 2n2 = (1 * n + 2n * n) + n + -45
7n + 2n2 = (1n + 2n2) + n + -45

Reorder the terms:
7n + 2n2 = -45 + 1n + n + 2n2

Combine like terms: 1n + n = 2n
7n + 2n2 = -45 + 2n + 2n2

Add '-2n2' to each side of the equation.
7n + 2n2 + -2n2 = -45 + 2n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
7n + 0 = -45 + 2n + 2n2 + -2n2
7n = -45 + 2n + 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
7n = -45 + 2n + 0
7n = -45 + 2n

Solving
7n = -45 + 2n

Solving for variable 'n'.

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

Add '-2n' to each side of the equation.
7n + -2n = -45 + 2n + -2n

Combine like terms: 7n + -2n = 5n
5n = -45 + 2n + -2n

Combine like terms: 2n + -2n = 0
5n = -45 + 0
5n = -45

Divide each side by '5'.
n = -9

Simplifying
n = -9

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