-6n(5n-1)=9-30n

Solution for -6n(5n-1)=9-30n equation:

Simplifying
-6n(5n + -1) = 9 + -30n

Reorder the terms:
-6n(-1 + 5n) = 9 + -30n
(-1 * -6n + 5n * -6n) = 9 + -30n
(6n + -30n2) = 9 + -30n

Solving
6n + -30n2 = 9 + -30n

Solving for variable 'n'.

Reorder the terms:
-9 + 6n + 30n + -30n2 = 9 + -30n + -9 + 30n

Combine like terms: 6n + 30n = 36n
-9 + 36n + -30n2 = 9 + -30n + -9 + 30n

Reorder the terms:
-9 + 36n + -30n2 = 9 + -9 + -30n + 30n

Combine like terms: 9 + -9 = 0
-9 + 36n + -30n2 = 0 + -30n + 30n
-9 + 36n + -30n2 = -30n + 30n

Combine like terms: -30n + 30n = 0
-9 + 36n + -30n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 12n + -10n2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-3 + 12n + -10n2)' equal to zero and attempt to solve:

Simplifying
-3 + 12n + -10n2 = 0

Solving
-3 + 12n + -10n2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
0.3 + -1.2n + n2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + -1.2n + -0.3 + n2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + -1.2n + n2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + -1.2n + n2 = 0.0 + -0.3
-1.2n + n2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
-1.2n + n2 = -0.3

The n term is -1.2n.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2n + 0.36 + n2 = -0.3 + 0.36

Reorder the terms:
0.36 + -1.2n + n2 = -0.3 + 0.36

Combine like terms: -0.3 + 0.36 = 0.06
0.36 + -1.2n + n2 = 0.06

Factor a perfect square on the left side:
(n + -0.6)(n + -0.6) = 0.06

Calculate the square root of the right side: 0.244948974

Break this problem into two subproblems by setting 
(n + -0.6) equal to 0.244948974 and -0.244948974.

Subproblem 1
n + -0.6 = 0.244948974

Simplifying
n + -0.6 = 0.244948974

Reorder the terms:
-0.6 + n = 0.244948974

Solving
-0.6 + n = 0.244948974

Solving for variable 'n'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + n = 0.244948974 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n = 0.244948974 + 0.6
n = 0.244948974 + 0.6

Combine like terms: 0.244948974 + 0.6 = 0.844948974
n = 0.844948974

Simplifying
n = 0.844948974

Subproblem 2
n + -0.6 = -0.244948974

Simplifying
n + -0.6 = -0.244948974

Reorder the terms:
-0.6 + n = -0.244948974

Solving
-0.6 + n = -0.244948974

Solving for variable 'n'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + n = -0.244948974 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + n = -0.244948974 + 0.6
n = -0.244948974 + 0.6

Combine like terms: -0.244948974 + 0.6 = 0.355051026
n = 0.355051026

Simplifying
n = 0.355051026

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.844948974, 0.355051026}
Solution
n = {0.844948974, 0.355051026}