-2(6n+7)5n=-150

Solution for -2(6n+7)5n=-150 equation:

Simplifying
-2(6n + 7) * 5n = -150

Reorder the terms:
-2(7 + 6n) * 5n = -150

Reorder the terms for easier multiplication:
-2 * 5n(7 + 6n) = -150

Multiply -2 * 5
-10n(7 + 6n) = -150
(7 * -10n + 6n * -10n) = -150
(-70n + -60n2) = -150

Solving
-70n + -60n2 = -150

Solving for variable 'n'.

Reorder the terms:
150 + -70n + -60n2 = -150 + 150

Combine like terms: -150 + 150 = 0
150 + -70n + -60n2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(15 + -7n + -6n2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(15 + -7n + -6n2)' equal to zero and attempt to solve:

Simplifying
15 + -7n + -6n2 = 0

Solving
15 + -7n + -6n2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-2.5 + 1.166666667n + n2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 1.166666667n + 2.5 + n2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 1.166666667n + n2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 1.166666667n + n2 = 0 + 2.5
1.166666667n + n2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
1.166666667n + n2 = 2.5

The n term is 1.166666667n.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667n + 0.3402777780 + n2 = 2.5 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667n + n2 = 2.5 + 0.3402777780

Combine like terms: 2.5 + 0.3402777780 = 2.840277778
0.3402777780 + 1.166666667n + n2 = 2.840277778

Factor a perfect square on the left side:
(n + 0.5833333335)(n + 0.5833333335) = 2.840277778

Calculate the square root of the right side: 1.685312368

Break this problem into two subproblems by setting 
(n + 0.5833333335) equal to 1.685312368 and -1.685312368.

Subproblem 1
n + 0.5833333335 = 1.685312368

Simplifying
n + 0.5833333335 = 1.685312368

Reorder the terms:
0.5833333335 + n = 1.685312368

Solving
0.5833333335 + n = 1.685312368

Solving for variable 'n'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + n = 1.685312368 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + n = 1.685312368 + -0.5833333335
n = 1.685312368 + -0.5833333335

Combine like terms: 1.685312368 + -0.5833333335 = 1.1019790345
n = 1.1019790345

Simplifying
n = 1.1019790345

Subproblem 2
n + 0.5833333335 = -1.685312368

Simplifying
n + 0.5833333335 = -1.685312368

Reorder the terms:
0.5833333335 + n = -1.685312368

Solving
0.5833333335 + n = -1.685312368

Solving for variable 'n'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + n = -1.685312368 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + n = -1.685312368 + -0.5833333335
n = -1.685312368 + -0.5833333335

Combine like terms: -1.685312368 + -0.5833333335 = -2.2686457015
n = -2.2686457015

Simplifying
n = -2.2686457015

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.1019790345, -2.2686457015}
Solution
n = {1.1019790345, -2.2686457015}