(n+1)(n-2)=(n+7)(n-2)

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Solution for (n+1)(n-2)=(n+7)(n-2) equation: 


Simplifying
(n + 1)(n + -2) = (n + 7)(n + -2)

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

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

Multiply (1 + n) * (-2 + n)
(1(-2 + n) + n(-2 + n)) = (n + 7)(n + -2)
((-2 * 1 + n * 1) + n(-2 + n)) = (n + 7)(n + -2)
((-2 + 1n) + n(-2 + n)) = (n + 7)(n + -2)
(-2 + 1n + (-2 * n + n * n)) = (n + 7)(n + -2)
(-2 + 1n + (-2n + n2)) = (n + 7)(n + -2)

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

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

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

Multiply (7 + n) * (-2 + n)
-2 + -1n + n2 = (7(-2 + n) + n(-2 + n))
-2 + -1n + n2 = ((-2 * 7 + n * 7) + n(-2 + n))
-2 + -1n + n2 = ((-14 + 7n) + n(-2 + n))
-2 + -1n + n2 = (-14 + 7n + (-2 * n + n * n))
-2 + -1n + n2 = (-14 + 7n + (-2n + n2))

Combine like terms: 7n + -2n = 5n
-2 + -1n + n2 = (-14 + 5n + n2)

Add '-1n2' to each side of the equation.
-2 + -1n + n2 + -1n2 = -14 + 5n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-2 + -1n + 0 = -14 + 5n + n2 + -1n2
-2 + -1n = -14 + 5n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-2 + -1n = -14 + 5n + 0
-2 + -1n = -14 + 5n

Solving
-2 + -1n = -14 + 5n

Solving for variable 'n'.

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

Add '-5n' to each side of the equation.
-2 + -1n + -5n = -14 + 5n + -5n

Combine like terms: -1n + -5n = -6n
-2 + -6n = -14 + 5n + -5n

Combine like terms: 5n + -5n = 0
-2 + -6n = -14 + 0
-2 + -6n = -14

Add '2' to each side of the equation.
-2 + 2 + -6n = -14 + 2

Combine like terms: -2 + 2 = 0
0 + -6n = -14 + 2
-6n = -14 + 2

Combine like terms: -14 + 2 = -12
-6n = -12

Divide each side by '-6'.
n = 2

Simplifying
n = 2

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