(n+5)(2n-9)=(n-1)(n+3)

Solution for (n+5)(2n-9)=(n-1)(n+3) equation:

Simplifying
(n + 5)(2n + -9) = (n + -1)(n + 3)

Reorder the terms:
(5 + n)(2n + -9) = (n + -1)(n + 3)

Reorder the terms:
(5 + n)(-9 + 2n) = (n + -1)(n + 3)

Multiply (5 + n) * (-9 + 2n)
(5(-9 + 2n) + n(-9 + 2n)) = (n + -1)(n + 3)
((-9 * 5 + 2n * 5) + n(-9 + 2n)) = (n + -1)(n + 3)
((-45 + 10n) + n(-9 + 2n)) = (n + -1)(n + 3)
(-45 + 10n + (-9 * n + 2n * n)) = (n + -1)(n + 3)
(-45 + 10n + (-9n + 2n2)) = (n + -1)(n + 3)

Combine like terms: 10n + -9n = 1n
(-45 + 1n + 2n2) = (n + -1)(n + 3)

Reorder the terms:
-45 + 1n + 2n2 = (-1 + n)(n + 3)

Reorder the terms:
-45 + 1n + 2n2 = (-1 + n)(3 + n)

Multiply (-1 + n) * (3 + n)
-45 + 1n + 2n2 = (-1(3 + n) + n(3 + n))
-45 + 1n + 2n2 = ((3 * -1 + n * -1) + n(3 + n))
-45 + 1n + 2n2 = ((-3 + -1n) + n(3 + n))
-45 + 1n + 2n2 = (-3 + -1n + (3 * n + n * n))
-45 + 1n + 2n2 = (-3 + -1n + (3n + n2))

Combine like terms: -1n + 3n = 2n
-45 + 1n + 2n2 = (-3 + 2n + n2)

Solving
-45 + 1n + 2n2 = -3 + 2n + n2

Solving for variable 'n'.

Reorder the terms:
-45 + 3 + 1n + -2n + 2n2 + -1n2 = -3 + 2n + n2 + 3 + -2n + -1n2

Combine like terms: -45 + 3 = -42
-42 + 1n + -2n + 2n2 + -1n2 = -3 + 2n + n2 + 3 + -2n + -1n2

Combine like terms: 1n + -2n = -1n
-42 + -1n + 2n2 + -1n2 = -3 + 2n + n2 + 3 + -2n + -1n2

Combine like terms: 2n2 + -1n2 = 1n2
-42 + -1n + 1n2 = -3 + 2n + n2 + 3 + -2n + -1n2

Reorder the terms:
-42 + -1n + 1n2 = -3 + 3 + 2n + -2n + n2 + -1n2

Combine like terms: -3 + 3 = 0
-42 + -1n + 1n2 = 0 + 2n + -2n + n2 + -1n2
-42 + -1n + 1n2 = 2n + -2n + n2 + -1n2

Combine like terms: 2n + -2n = 0
-42 + -1n + 1n2 = 0 + n2 + -1n2
-42 + -1n + 1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-42 + -1n + 1n2 = 0

Factor a trinomial.
(-6 + -1n)(7 + -1n) = 0

Subproblem 1
Set the factor '(-6 + -1n)' equal to zero and attempt to solve:

Simplifying
-6 + -1n = 0

Solving
-6 + -1n = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1n = 0 + 6
-1n = 0 + 6

Combine like terms: 0 + 6 = 6
-1n = 6

Divide each side by '-1'.
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {-6, 7}