f+2f(f+2.50)=11.25

Solution for f+2f(f+2.50)=11.25 equation:

Simplifying
f + 2f(f + 2.50) = 11.25

Reorder the terms:
f + 2f(2.50 + f) = 11.25
f + (2.50 * 2f + f * 2f) = 11.25
f + (5f + 2f2) = 11.25

Combine like terms: f + 5f = 6f
6f + 2f2 = 11.25

Solving
6f + 2f2 = 11.25

Solving for variable 'f'.

Reorder the terms:
-11.25 + 6f + 2f2 = 11.25 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
-11.25 + 6f + 2f2 = 0.00

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

Divide each side by '2'.
-5.625 + 3f + f2 = 0.00

Move the constant term to the right:

Add '5.625' to each side of the equation.
-5.625 + 3f + 5.625 + f2 = 0.00 + 5.625

Reorder the terms:
-5.625 + 5.625 + 3f + f2 = 0.00 + 5.625

Combine like terms: -5.625 + 5.625 = 0.000
0.000 + 3f + f2 = 0.00 + 5.625
3f + f2 = 0.00 + 5.625

Combine like terms: 0.00 + 5.625 = 5.625
3f + f2 = 5.625

The f term is 3f.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3f + 2.25 + f2 = 5.625 + 2.25

Reorder the terms:
2.25 + 3f + f2 = 5.625 + 2.25

Combine like terms: 5.625 + 2.25 = 7.875
2.25 + 3f + f2 = 7.875

Factor a perfect square on the left side:
(f + 1.5)(f + 1.5) = 7.875

Calculate the square root of the right side: 2.80624304

Break this problem into two subproblems by setting 
(f + 1.5) equal to 2.80624304 and -2.80624304.

Subproblem 1
f + 1.5 = 2.80624304

Simplifying
f + 1.5 = 2.80624304

Reorder the terms:
1.5 + f = 2.80624304

Solving
1.5 + f = 2.80624304

Solving for variable 'f'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + f = 2.80624304 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + f = 2.80624304 + -1.5
f = 2.80624304 + -1.5

Combine like terms: 2.80624304 + -1.5 = 1.30624304
f = 1.30624304

Simplifying
f = 1.30624304

Subproblem 2
f + 1.5 = -2.80624304

Simplifying
f + 1.5 = -2.80624304

Reorder the terms:
1.5 + f = -2.80624304

Solving
1.5 + f = -2.80624304

Solving for variable 'f'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + f = -2.80624304 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + f = -2.80624304 + -1.5
f = -2.80624304 + -1.5

Combine like terms: -2.80624304 + -1.5 = -4.30624304
f = -4.30624304

Simplifying
f = -4.30624304

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {1.30624304, -4.30624304}