21+7n=3(1+4n)4n

Solution for 21+7n=3(1+4n)4n equation:

Simplifying
21 + 7n = 3(1 + 4n) * 4n

Reorder the terms for easier multiplication:
21 + 7n = 3 * 4n(1 + 4n)

Multiply 3 * 4
21 + 7n = 12n(1 + 4n)
21 + 7n = (1 * 12n + 4n * 12n)
21 + 7n = (12n + 48n2)

Solving
21 + 7n = 12n + 48n2

Solving for variable 'n'.

Combine like terms: 7n + -12n = -5n
21 + -5n + -48n2 = 12n + 48n2 + -12n + -48n2

Reorder the terms:
21 + -5n + -48n2 = 12n + -12n + 48n2 + -48n2

Combine like terms: 12n + -12n = 0
21 + -5n + -48n2 = 0 + 48n2 + -48n2
21 + -5n + -48n2 = 48n2 + -48n2

Combine like terms: 48n2 + -48n2 = 0
21 + -5n + -48n2 = 0

Begin completing the square.  Divide all terms by
-48 the coefficient of the squared term: 

Divide each side by '-48'.
-0.4375 + 0.1041666667n + n2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + 0.1041666667n + 0.4375 + n2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + 0.1041666667n + n2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + 0.1041666667n + n2 = 0 + 0.4375
0.1041666667n + n2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
0.1041666667n + n2 = 0.4375

The n term is 0.1041666667n.  Take half its coefficient (0.05208333335).
Square it (0.002712673613) and add it to both sides.

Add '0.002712673613' to each side of the equation.
0.1041666667n + 0.002712673613 + n2 = 0.4375 + 0.002712673613

Reorder the terms:
0.002712673613 + 0.1041666667n + n2 = 0.4375 + 0.002712673613

Combine like terms: 0.4375 + 0.002712673613 = 0.440212673613
0.002712673613 + 0.1041666667n + n2 = 0.440212673613

Factor a perfect square on the left side:
(n + 0.05208333335)(n + 0.05208333335) = 0.440212673613

Calculate the square root of the right side: 0.663485247

Break this problem into two subproblems by setting 
(n + 0.05208333335) equal to 0.663485247 and -0.663485247.

Subproblem 1
n + 0.05208333335 = 0.663485247

Simplifying
n + 0.05208333335 = 0.663485247

Reorder the terms:
0.05208333335 + n = 0.663485247

Solving
0.05208333335 + n = 0.663485247

Solving for variable 'n'.

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

Add '-0.05208333335' to each side of the equation.
0.05208333335 + -0.05208333335 + n = 0.663485247 + -0.05208333335

Combine like terms: 0.05208333335 + -0.05208333335 = 0.00000000000
0.00000000000 + n = 0.663485247 + -0.05208333335
n = 0.663485247 + -0.05208333335

Combine like terms: 0.663485247 + -0.05208333335 = 0.61140191365
n = 0.61140191365

Simplifying
n = 0.61140191365

Subproblem 2
n + 0.05208333335 = -0.663485247

Simplifying
n + 0.05208333335 = -0.663485247

Reorder the terms:
0.05208333335 + n = -0.663485247

Solving
0.05208333335 + n = -0.663485247

Solving for variable 'n'.

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

Add '-0.05208333335' to each side of the equation.
0.05208333335 + -0.05208333335 + n = -0.663485247 + -0.05208333335

Combine like terms: 0.05208333335 + -0.05208333335 = 0.00000000000
0.00000000000 + n = -0.663485247 + -0.05208333335
n = -0.663485247 + -0.05208333335

Combine like terms: -0.663485247 + -0.05208333335 = -0.71556858035
n = -0.71556858035

Simplifying
n = -0.71556858035

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.61140191365, -0.71556858035}