12=(7n-2)(n+3)

Solution for 12=(7n-2)(n+3) equation:

Simplifying
12 = (7n + -2)(n + 3)

Reorder the terms:
12 = (-2 + 7n)(n + 3)

Reorder the terms:
12 = (-2 + 7n)(3 + n)

Multiply (-2 + 7n) * (3 + n)
12 = (-2(3 + n) + 7n * (3 + n))
12 = ((3 * -2 + n * -2) + 7n * (3 + n))
12 = ((-6 + -2n) + 7n * (3 + n))
12 = (-6 + -2n + (3 * 7n + n * 7n))
12 = (-6 + -2n + (21n + 7n2))

Combine like terms: -2n + 21n = 19n
12 = (-6 + 19n + 7n2)

Solving
12 = -6 + 19n + 7n2

Solving for variable 'n'.

Combine like terms: 12 + 6 = 18
18 + -19n + -7n2 = -6 + 19n + 7n2 + 6 + -19n + -7n2

Reorder the terms:
18 + -19n + -7n2 = -6 + 6 + 19n + -19n + 7n2 + -7n2

Combine like terms: -6 + 6 = 0
18 + -19n + -7n2 = 0 + 19n + -19n + 7n2 + -7n2
18 + -19n + -7n2 = 19n + -19n + 7n2 + -7n2

Combine like terms: 19n + -19n = 0
18 + -19n + -7n2 = 0 + 7n2 + -7n2
18 + -19n + -7n2 = 7n2 + -7n2

Combine like terms: 7n2 + -7n2 = 0
18 + -19n + -7n2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
-2.571428571 + 2.714285714n + n2 = 0

Move the constant term to the right:

Add '2.571428571' to each side of the equation.
-2.571428571 + 2.714285714n + 2.571428571 + n2 = 0 + 2.571428571

Reorder the terms:
-2.571428571 + 2.571428571 + 2.714285714n + n2 = 0 + 2.571428571

Combine like terms: -2.571428571 + 2.571428571 = 0.000000000
0.000000000 + 2.714285714n + n2 = 0 + 2.571428571
2.714285714n + n2 = 0 + 2.571428571

Combine like terms: 0 + 2.571428571 = 2.571428571
2.714285714n + n2 = 2.571428571

The n term is 2.714285714n.  Take half its coefficient (1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
2.714285714n + 1.841836734 + n2 = 2.571428571 + 1.841836734

Reorder the terms:
1.841836734 + 2.714285714n + n2 = 2.571428571 + 1.841836734

Combine like terms: 2.571428571 + 1.841836734 = 4.413265305
1.841836734 + 2.714285714n + n2 = 4.413265305

Factor a perfect square on the left side:
(n + 1.357142857)(n + 1.357142857) = 4.413265305

Calculate the square root of the right side: 2.10077731

Break this problem into two subproblems by setting 
(n + 1.357142857) equal to 2.10077731 and -2.10077731.

Subproblem 1
n + 1.357142857 = 2.10077731

Simplifying
n + 1.357142857 = 2.10077731

Reorder the terms:
1.357142857 + n = 2.10077731

Solving
1.357142857 + n = 2.10077731

Solving for variable 'n'.

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

Add '-1.357142857' to each side of the equation.
1.357142857 + -1.357142857 + n = 2.10077731 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + n = 2.10077731 + -1.357142857
n = 2.10077731 + -1.357142857

Combine like terms: 2.10077731 + -1.357142857 = 0.743634453
n = 0.743634453

Simplifying
n = 0.743634453

Subproblem 2
n + 1.357142857 = -2.10077731

Simplifying
n + 1.357142857 = -2.10077731

Reorder the terms:
1.357142857 + n = -2.10077731

Solving
1.357142857 + n = -2.10077731

Solving for variable 'n'.

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

Add '-1.357142857' to each side of the equation.
1.357142857 + -1.357142857 + n = -2.10077731 + -1.357142857

Combine like terms: 1.357142857 + -1.357142857 = 0.000000000
0.000000000 + n = -2.10077731 + -1.357142857
n = -2.10077731 + -1.357142857

Combine like terms: -2.10077731 + -1.357142857 = -3.457920167
n = -3.457920167

Simplifying
n = -3.457920167

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.743634453, -3.457920167}