(6n+3)2+(6n+4)2+(6n+5)2=

Solution for (6n+3)2+(6n+4)2+(6n+5)2= equation:

Simplifying
(6n + 3) * 2 + (6n + 4) * 2 + (6n + 5) * 2 = 0

Reorder the terms:
(3 + 6n) * 2 + (6n + 4) * 2 + (6n + 5) * 2 = 0

Reorder the terms for easier multiplication:
2(3 + 6n) + (6n + 4) * 2 + (6n + 5) * 2 = 0
(3 * 2 + 6n * 2) + (6n + 4) * 2 + (6n + 5) * 2 = 0
(6 + 12n) + (6n + 4) * 2 + (6n + 5) * 2 = 0

Reorder the terms:
6 + 12n + (4 + 6n) * 2 + (6n + 5) * 2 = 0

Reorder the terms for easier multiplication:
6 + 12n + 2(4 + 6n) + (6n + 5) * 2 = 0
6 + 12n + (4 * 2 + 6n * 2) + (6n + 5) * 2 = 0
6 + 12n + (8 + 12n) + (6n + 5) * 2 = 0

Reorder the terms:
6 + 12n + 8 + 12n + (5 + 6n) * 2 = 0

Reorder the terms for easier multiplication:
6 + 12n + 8 + 12n + 2(5 + 6n) = 0
6 + 12n + 8 + 12n + (5 * 2 + 6n * 2) = 0
6 + 12n + 8 + 12n + (10 + 12n) = 0

Reorder the terms:
6 + 8 + 10 + 12n + 12n + 12n = 0

Combine like terms: 6 + 8 = 14
14 + 10 + 12n + 12n + 12n = 0

Combine like terms: 14 + 10 = 24
24 + 12n + 12n + 12n = 0

Combine like terms: 12n + 12n = 24n
24 + 24n + 12n = 0

Combine like terms: 24n + 12n = 36n
24 + 36n = 0

Solving
24 + 36n = 0

Solving for variable 'n'.

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

Add '-24' to each side of the equation.
24 + -24 + 36n = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 36n = 0 + -24
36n = 0 + -24

Combine like terms: 0 + -24 = -24
36n = -24

Divide each side by '36'.
n = -0.6666666667

Simplifying
n = -0.6666666667