4(1-3n)-14=4(2n+3)9n

Solution for 4(1-3n)-14=4(2n+3)9n equation:

Simplifying
4(1 + -3n) + -14 = 4(2n + 3) * 9n
(1 * 4 + -3n * 4) + -14 = 4(2n + 3) * 9n
(4 + -12n) + -14 = 4(2n + 3) * 9n

Reorder the terms:
4 + -14 + -12n = 4(2n + 3) * 9n

Combine like terms: 4 + -14 = -10
-10 + -12n = 4(2n + 3) * 9n

Reorder the terms:
-10 + -12n = 4(3 + 2n) * 9n

Reorder the terms for easier multiplication:
-10 + -12n = 4 * 9n(3 + 2n)

Multiply 4 * 9
-10 + -12n = 36n(3 + 2n)
-10 + -12n = (3 * 36n + 2n * 36n)
-10 + -12n = (108n + 72n2)

Solving
-10 + -12n = 108n + 72n2

Solving for variable 'n'.

Combine like terms: -12n + -108n = -120n
-10 + -120n + -72n2 = 108n + 72n2 + -108n + -72n2

Reorder the terms:
-10 + -120n + -72n2 = 108n + -108n + 72n2 + -72n2

Combine like terms: 108n + -108n = 0
-10 + -120n + -72n2 = 0 + 72n2 + -72n2
-10 + -120n + -72n2 = 72n2 + -72n2

Combine like terms: 72n2 + -72n2 = 0
-10 + -120n + -72n2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(5 + 60n + 36n2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(5 + 60n + 36n2)' equal to zero and attempt to solve:

Simplifying
5 + 60n + 36n2 = 0

Solving
5 + 60n + 36n2 = 0

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

Divide each side by '36'.
0.1388888889 + 1.666666667n + n2 = 0

Move the constant term to the right:

Add '-0.1388888889' to each side of the equation.
0.1388888889 + 1.666666667n + -0.1388888889 + n2 = 0 + -0.1388888889

Reorder the terms:
0.1388888889 + -0.1388888889 + 1.666666667n + n2 = 0 + -0.1388888889

Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000
0.0000000000 + 1.666666667n + n2 = 0 + -0.1388888889
1.666666667n + n2 = 0 + -0.1388888889

Combine like terms: 0 + -0.1388888889 = -0.1388888889
1.666666667n + n2 = -0.1388888889

The n term is 1.666666667n.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667n + 0.6944444447 + n2 = -0.1388888889 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667n + n2 = -0.1388888889 + 0.6944444447

Combine like terms: -0.1388888889 + 0.6944444447 = 0.5555555558
0.6944444447 + 1.666666667n + n2 = 0.5555555558

Factor a perfect square on the left side:
(n + 0.8333333335)(n + 0.8333333335) = 0.5555555558

Calculate the square root of the right side: 0.745355993

Break this problem into two subproblems by setting 
(n + 0.8333333335) equal to 0.745355993 and -0.745355993.

Subproblem 1
n + 0.8333333335 = 0.745355993

Simplifying
n + 0.8333333335 = 0.745355993

Reorder the terms:
0.8333333335 + n = 0.745355993

Solving
0.8333333335 + n = 0.745355993

Solving for variable 'n'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + n = 0.745355993 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + n = 0.745355993 + -0.8333333335
n = 0.745355993 + -0.8333333335

Combine like terms: 0.745355993 + -0.8333333335 = -0.0879773405
n = -0.0879773405

Simplifying
n = -0.0879773405

Subproblem 2
n + 0.8333333335 = -0.745355993

Simplifying
n + 0.8333333335 = -0.745355993

Reorder the terms:
0.8333333335 + n = -0.745355993

Solving
0.8333333335 + n = -0.745355993

Solving for variable 'n'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + n = -0.745355993 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + n = -0.745355993 + -0.8333333335
n = -0.745355993 + -0.8333333335

Combine like terms: -0.745355993 + -0.8333333335 = -1.5786893265
n = -1.5786893265

Simplifying
n = -1.5786893265

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.0879773405, -1.5786893265}
Solution
n = {-0.0879773405, -1.5786893265}