(n+6)((n+6)-10)=200

Solution for (n+6)((n+6)-10)=200 equation:

Simplifying
(n + 6)((n + 6) + -10) = 200

Reorder the terms:
(6 + n)((n + 6) + -10) = 200

Reorder the terms:
(6 + n)((6 + n) + -10) = 200

Remove parenthesis around (6 + n)
(6 + n)(6 + n + -10) = 200

Reorder the terms:
(6 + n)(6 + -10 + n) = 200

Combine like terms: 6 + -10 = -4
(6 + n)(-4 + n) = 200

Multiply (6 + n) * (-4 + n)
(6(-4 + n) + n(-4 + n)) = 200
((-4 * 6 + n * 6) + n(-4 + n)) = 200
((-24 + 6n) + n(-4 + n)) = 200
(-24 + 6n + (-4 * n + n * n)) = 200
(-24 + 6n + (-4n + n2)) = 200

Combine like terms: 6n + -4n = 2n
(-24 + 2n + n2) = 200

Solving
-24 + 2n + n2 = 200

Solving for variable 'n'.

Reorder the terms:
-24 + -200 + 2n + n2 = 200 + -200

Combine like terms: -24 + -200 = -224
-224 + 2n + n2 = 200 + -200

Combine like terms: 200 + -200 = 0
-224 + 2n + n2 = 0

Factor a trinomial.
(-16 + -1n)(14 + -1n) = 0

Subproblem 1
Set the factor '(-16 + -1n)' equal to zero and attempt to solve:

Simplifying
-16 + -1n = 0

Solving
-16 + -1n = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1n = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1n = 0 + 16
-1n = 0 + 16

Combine like terms: 0 + 16 = 16
-1n = 16

Divide each side by '-1'.
n = -16

Simplifying
n = -16
Subproblem 2
Set the factor '(14 + -1n)' equal to zero and attempt to solve:

Simplifying
14 + -1n = 0

Solving
14 + -1n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1n = 0 + -14
-1n = 0 + -14

Combine like terms: 0 + -14 = -14
-1n = -14

Divide each side by '-1'.
n = 14

Simplifying
n = 14
Solution
n = {-16, 14}