(n+5)(n-3)=(n+1)(n-6)

Solution for (n+5)(n-3)=(n+1)(n-6) equation:

Simplifying
(n + 5)(n + -3) = (n + 1)(n + -6)

Reorder the terms:
(5 + n)(n + -3) = (n + 1)(n + -6)

Reorder the terms:
(5 + n)(-3 + n) = (n + 1)(n + -6)

Multiply (5 + n) * (-3 + n)
(5(-3 + n) + n(-3 + n)) = (n + 1)(n + -6)
((-3 * 5 + n * 5) + n(-3 + n)) = (n + 1)(n + -6)
((-15 + 5n) + n(-3 + n)) = (n + 1)(n + -6)
(-15 + 5n + (-3 * n + n * n)) = (n + 1)(n + -6)
(-15 + 5n + (-3n + n2)) = (n + 1)(n + -6)

Combine like terms: 5n + -3n = 2n
(-15 + 2n + n2) = (n + 1)(n + -6)

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

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

Multiply (1 + n) * (-6 + n)
-15 + 2n + n2 = (1(-6 + n) + n(-6 + n))
-15 + 2n + n2 = ((-6 * 1 + n * 1) + n(-6 + n))
-15 + 2n + n2 = ((-6 + 1n) + n(-6 + n))
-15 + 2n + n2 = (-6 + 1n + (-6 * n + n * n))
-15 + 2n + n2 = (-6 + 1n + (-6n + n2))

Combine like terms: 1n + -6n = -5n
-15 + 2n + n2 = (-6 + -5n + n2)

Add '-1n2' to each side of the equation.
-15 + 2n + n2 + -1n2 = -6 + -5n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-15 + 2n + 0 = -6 + -5n + n2 + -1n2
-15 + 2n = -6 + -5n + n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-15 + 2n = -6 + -5n + 0
-15 + 2n = -6 + -5n

Solving
-15 + 2n = -6 + -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.
-15 + 2n + 5n = -6 + -5n + 5n

Combine like terms: 2n + 5n = 7n
-15 + 7n = -6 + -5n + 5n

Combine like terms: -5n + 5n = 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 = 9
7n = 9

Divide each side by '7'.
n = 1.285714286

Simplifying
n = 1.285714286