-4f^2+100f-108=0

Solution for -4f^2+100f-108=0 equation:

Simplifying
-4f2 + 100f + -108 = 0

Reorder the terms:
-108 + 100f + -4f2 = 0

Solving
-108 + 100f + -4f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-27 + 25f + -1f2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-27 + 25f + -1f2)' equal to zero and attempt to solve:

Simplifying
-27 + 25f + -1f2 = 0

Solving
-27 + 25f + -1f2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
27 + -25f + f2 = 0

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -25f + -27 + f2 = 0 + -27

Reorder the terms:
27 + -27 + -25f + f2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -25f + f2 = 0 + -27
-25f + f2 = 0 + -27

Combine like terms: 0 + -27 = -27
-25f + f2 = -27

The f term is -25f.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25f + 156.25 + f2 = -27 + 156.25

Reorder the terms:
156.25 + -25f + f2 = -27 + 156.25

Combine like terms: -27 + 156.25 = 129.25
156.25 + -25f + f2 = 129.25

Factor a perfect square on the left side:
(f + -12.5)(f + -12.5) = 129.25

Calculate the square root of the right side: 11.368817001

Break this problem into two subproblems by setting 
(f + -12.5) equal to 11.368817001 and -11.368817001.

Subproblem 1
f + -12.5 = 11.368817001

Simplifying
f + -12.5 = 11.368817001

Reorder the terms:
-12.5 + f = 11.368817001

Solving
-12.5 + f = 11.368817001

Solving for variable 'f'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + f = 11.368817001 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + f = 11.368817001 + 12.5
f = 11.368817001 + 12.5

Combine like terms: 11.368817001 + 12.5 = 23.868817001
f = 23.868817001

Simplifying
f = 23.868817001

Subproblem 2
f + -12.5 = -11.368817001

Simplifying
f + -12.5 = -11.368817001

Reorder the terms:
-12.5 + f = -11.368817001

Solving
-12.5 + f = -11.368817001

Solving for variable 'f'.

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

Add '12.5' to each side of the equation.
-12.5 + 12.5 + f = -11.368817001 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + f = -11.368817001 + 12.5
f = -11.368817001 + 12.5

Combine like terms: -11.368817001 + 12.5 = 1.131182999
f = 1.131182999

Simplifying
f = 1.131182999

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {23.868817001, 1.131182999}
Solution
f = {23.868817001, 1.131182999}