.2f+.6f(f+20)=-8+.4f

Solution for .2f+.6f(f+20)=-8+.4f equation:

Simplifying
0.2f + 0.6f(f + 20) = -8 + 0.4f

Reorder the terms:
0.2f + 0.6f(20 + f) = -8 + 0.4f
0.2f + (20 * 0.6f + f * 0.6f) = -8 + 0.4f
0.2f + (12f + 0.6f2) = -8 + 0.4f

Combine like terms: 0.2f + 12f = 12.2f
12.2f + 0.6f2 = -8 + 0.4f

Solving
12.2f + 0.6f2 = -8 + 0.4f

Solving for variable 'f'.

Reorder the terms:
8 + 12.2f + -0.4f + 0.6f2 = -8 + 0.4f + 8 + -0.4f

Combine like terms: 12.2f + -0.4f = 11.8f
8 + 11.8f + 0.6f2 = -8 + 0.4f + 8 + -0.4f

Reorder the terms:
8 + 11.8f + 0.6f2 = -8 + 8 + 0.4f + -0.4f

Combine like terms: -8 + 8 = 0
8 + 11.8f + 0.6f2 = 0 + 0.4f + -0.4f
8 + 11.8f + 0.6f2 = 0.4f + -0.4f

Combine like terms: 0.4f + -0.4f = 0.0
8 + 11.8f + 0.6f2 = 0.0

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

Divide each side by '0.6'.
13.33333333 + 19.66666667f + f2 = 0

Move the constant term to the right:

Add '-13.33333333' to each side of the equation.
13.33333333 + 19.66666667f + -13.33333333 + f2 = 0 + -13.33333333

Reorder the terms:
13.33333333 + -13.33333333 + 19.66666667f + f2 = 0 + -13.33333333

Combine like terms: 13.33333333 + -13.33333333 = 0.00000000
0.00000000 + 19.66666667f + f2 = 0 + -13.33333333
19.66666667f + f2 = 0 + -13.33333333

Combine like terms: 0 + -13.33333333 = -13.33333333
19.66666667f + f2 = -13.33333333

The f term is 19.66666667f.  Take half its coefficient (9.833333335).
Square it (96.69444448) and add it to both sides.

Add '96.69444448' to each side of the equation.
19.66666667f + 96.69444448 + f2 = -13.33333333 + 96.69444448

Reorder the terms:
96.69444448 + 19.66666667f + f2 = -13.33333333 + 96.69444448

Combine like terms: -13.33333333 + 96.69444448 = 83.36111115
96.69444448 + 19.66666667f + f2 = 83.36111115

Factor a perfect square on the left side:
(f + 9.833333335)(f + 9.833333335) = 83.36111115

Calculate the square root of the right side: 9.130230619

Break this problem into two subproblems by setting 
(f + 9.833333335) equal to 9.130230619 and -9.130230619.

Subproblem 1
f + 9.833333335 = 9.130230619

Simplifying
f + 9.833333335 = 9.130230619

Reorder the terms:
9.833333335 + f = 9.130230619

Solving
9.833333335 + f = 9.130230619

Solving for variable 'f'.

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

Add '-9.833333335' to each side of the equation.
9.833333335 + -9.833333335 + f = 9.130230619 + -9.833333335

Combine like terms: 9.833333335 + -9.833333335 = 0.000000000
0.000000000 + f = 9.130230619 + -9.833333335
f = 9.130230619 + -9.833333335

Combine like terms: 9.130230619 + -9.833333335 = -0.703102716
f = -0.703102716

Simplifying
f = -0.703102716

Subproblem 2
f + 9.833333335 = -9.130230619

Simplifying
f + 9.833333335 = -9.130230619

Reorder the terms:
9.833333335 + f = -9.130230619

Solving
9.833333335 + f = -9.130230619

Solving for variable 'f'.

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

Add '-9.833333335' to each side of the equation.
9.833333335 + -9.833333335 + f = -9.130230619 + -9.833333335

Combine like terms: 9.833333335 + -9.833333335 = 0.000000000
0.000000000 + f = -9.130230619 + -9.833333335
f = -9.130230619 + -9.833333335

Combine like terms: -9.130230619 + -9.833333335 = -18.963563954
f = -18.963563954

Simplifying
f = -18.963563954

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {-0.703102716, -18.963563954}