3*(6f^2+12f+1)=

Solution for 3*(6f^2+12f+1)= equation:

Simplifying
3(6f2 + 12f + 1) = 0

Reorder the terms:
3(1 + 12f + 6f2) = 0
(1 * 3 + 12f * 3 + 6f2 * 3) = 0
(3 + 36f + 18f2) = 0

Solving
3 + 36f + 18f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 12f + 6f2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(1 + 12f + 6f2)' equal to zero and attempt to solve:

Simplifying
1 + 12f + 6f2 = 0

Solving
1 + 12f + 6f2 = 0

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

Divide each side by '6'.
0.1666666667 + 2f + f2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 2f + -0.1666666667 + f2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 2f + f2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 2f + f2 = 0 + -0.1666666667
2f + f2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
2f + f2 = -0.1666666667

The f term is 2f.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2f + 1 + f2 = -0.1666666667 + 1

Reorder the terms:
1 + 2f + f2 = -0.1666666667 + 1

Combine like terms: -0.1666666667 + 1 = 0.8333333333
1 + 2f + f2 = 0.8333333333

Factor a perfect square on the left side:
(f + 1)(f + 1) = 0.8333333333

Calculate the square root of the right side: 0.912870929

Break this problem into two subproblems by setting 
(f + 1) equal to 0.912870929 and -0.912870929.

Subproblem 1
f + 1 = 0.912870929

Simplifying
f + 1 = 0.912870929

Reorder the terms:
1 + f = 0.912870929

Solving
1 + f = 0.912870929

Solving for variable 'f'.

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

Add '-1' to each side of the equation.
1 + -1 + f = 0.912870929 + -1

Combine like terms: 1 + -1 = 0
0 + f = 0.912870929 + -1
f = 0.912870929 + -1

Combine like terms: 0.912870929 + -1 = -0.087129071
f = -0.087129071

Simplifying
f = -0.087129071

Subproblem 2
f + 1 = -0.912870929

Simplifying
f + 1 = -0.912870929

Reorder the terms:
1 + f = -0.912870929

Solving
1 + f = -0.912870929

Solving for variable 'f'.

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

Add '-1' to each side of the equation.
1 + -1 + f = -0.912870929 + -1

Combine like terms: 1 + -1 = 0
0 + f = -0.912870929 + -1
f = -0.912870929 + -1

Combine like terms: -0.912870929 + -1 = -1.912870929
f = -1.912870929

Simplifying
f = -1.912870929

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {-0.087129071, -1.912870929}
Solution
f = {-0.087129071, -1.912870929}