6(n+4)=2n^2-10

Solution for 6(n+4)=2n^2-10 equation:

Simplifying
6(n + 4) = 2n2 + -10

Reorder the terms:
6(4 + n) = 2n2 + -10
(4 * 6 + n * 6) = 2n2 + -10
(24 + 6n) = 2n2 + -10

Reorder the terms:
24 + 6n = -10 + 2n2

Solving
24 + 6n = -10 + 2n2

Solving for variable 'n'.

Reorder the terms:
24 + 10 + 6n + -2n2 = -10 + 2n2 + 10 + -2n2

Combine like terms: 24 + 10 = 34
34 + 6n + -2n2 = -10 + 2n2 + 10 + -2n2

Reorder the terms:
34 + 6n + -2n2 = -10 + 10 + 2n2 + -2n2

Combine like terms: -10 + 10 = 0
34 + 6n + -2n2 = 0 + 2n2 + -2n2
34 + 6n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
34 + 6n + -2n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + 3n + -1n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(17 + 3n + -1n2)' equal to zero and attempt to solve:

Simplifying
17 + 3n + -1n2 = 0

Solving
17 + 3n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-17 + -3n + n2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -3n + 17 + n2 = 0 + 17

Reorder the terms:
-17 + 17 + -3n + n2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -3n + n2 = 0 + 17
-3n + n2 = 0 + 17

Combine like terms: 0 + 17 = 17
-3n + n2 = 17

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 17 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 17 + 2.25

Combine like terms: 17 + 2.25 = 19.25
2.25 + -3n + n2 = 19.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(n + -1.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
n + -1.5 = 4.387482194

Simplifying
n + -1.5 = 4.387482194

Reorder the terms:
-1.5 + n = 4.387482194

Solving
-1.5 + n = 4.387482194

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = 4.387482194 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = 4.387482194 + 1.5
n = 4.387482194 + 1.5

Combine like terms: 4.387482194 + 1.5 = 5.887482194
n = 5.887482194

Simplifying
n = 5.887482194

Subproblem 2
n + -1.5 = -4.387482194

Simplifying
n + -1.5 = -4.387482194

Reorder the terms:
-1.5 + n = -4.387482194

Solving
-1.5 + n = -4.387482194

Solving for variable 'n'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + n = -4.387482194 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + n = -4.387482194 + 1.5
n = -4.387482194 + 1.5

Combine like terms: -4.387482194 + 1.5 = -2.887482194
n = -2.887482194

Simplifying
n = -2.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.887482194, -2.887482194}
Solution
n = {5.887482194, -2.887482194}