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

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

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

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

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

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

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

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

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

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

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