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

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


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

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

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

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

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

Reorder the terms:
-6 + -5n + n2 = (-3 + n)(n + 5)

Reorder the terms:
-6 + -5n + n2 = (-3 + n)(5 + n)

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

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

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

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

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

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

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

Combine like terms: 2n + -2n = 0
-6 + -7n = -15 + 0
-6 + -7n = -15

Add '6' to each side of the equation.
-6 + 6 + -7n = -15 + 6

Combine like terms: -6 + 6 = 0
0 + -7n = -15 + 6
-7n = -15 + 6

Combine like terms: -15 + 6 = -9
-7n = -9

Divide each side by '-7'.
n = 1.285714286

Simplifying
n = 1.285714286

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