-4f(f+6)+14=20

Solution for -4f(f+6)+14=20 equation:

Simplifying
-4f(f + 6) + 14 = 20

Reorder the terms:
-4f(6 + f) + 14 = 20
(6 * -4f + f * -4f) + 14 = 20
(-24f + -4f2) + 14 = 20

Reorder the terms:
14 + -24f + -4f2 = 20

Solving
14 + -24f + -4f2 = 20

Solving for variable 'f'.

Reorder the terms:
14 + -20 + -24f + -4f2 = 20 + -20

Combine like terms: 14 + -20 = -6
-6 + -24f + -4f2 = 20 + -20

Combine like terms: 20 + -20 = 0
-6 + -24f + -4f2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 12f + 2f2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 12f + 2f2)' equal to zero and attempt to solve:

Simplifying
3 + 12f + 2f2 = 0

Solving
3 + 12f + 2f2 = 0

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

Divide each side by '2'.
1.5 + 6f + f2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 6f + -1.5 + f2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 6f + f2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 6f + f2 = 0 + -1.5
6f + f2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
6f + f2 = -1.5

The f term is 6f.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6f + 9 + f2 = -1.5 + 9

Reorder the terms:
9 + 6f + f2 = -1.5 + 9

Combine like terms: -1.5 + 9 = 7.5
9 + 6f + f2 = 7.5

Factor a perfect square on the left side:
(f + 3)(f + 3) = 7.5

Calculate the square root of the right side: 2.738612788

Break this problem into two subproblems by setting 
(f + 3) equal to 2.738612788 and -2.738612788.

Subproblem 1
f + 3 = 2.738612788

Simplifying
f + 3 = 2.738612788

Reorder the terms:
3 + f = 2.738612788

Solving
3 + f = 2.738612788

Solving for variable 'f'.

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

Add '-3' to each side of the equation.
3 + -3 + f = 2.738612788 + -3

Combine like terms: 3 + -3 = 0
0 + f = 2.738612788 + -3
f = 2.738612788 + -3

Combine like terms: 2.738612788 + -3 = -0.261387212
f = -0.261387212

Simplifying
f = -0.261387212

Subproblem 2
f + 3 = -2.738612788

Simplifying
f + 3 = -2.738612788

Reorder the terms:
3 + f = -2.738612788

Solving
3 + f = -2.738612788

Solving for variable 'f'.

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

Add '-3' to each side of the equation.
3 + -3 + f = -2.738612788 + -3

Combine like terms: 3 + -3 = 0
0 + f = -2.738612788 + -3
f = -2.738612788 + -3

Combine like terms: -2.738612788 + -3 = -5.738612788
f = -5.738612788

Simplifying
f = -5.738612788

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {-0.261387212, -5.738612788}
Solution
f = {-0.261387212, -5.738612788}