1.2f(f+4)=2.4f+1.2

Solution for 1.2f(f+4)=2.4f+1.2 equation:

Simplifying
1.2f(f + 4) = 2.4f + 1.2

Reorder the terms:
1.2f(4 + f) = 2.4f + 1.2
(4 * 1.2f + f * 1.2f) = 2.4f + 1.2
(4.8f + 1.2f2) = 2.4f + 1.2

Reorder the terms:
4.8f + 1.2f2 = 1.2 + 2.4f

Solving
4.8f + 1.2f2 = 1.2 + 2.4f

Solving for variable 'f'.

Reorder the terms:
-1.2 + 4.8f + -2.4f + 1.2f2 = 1.2 + 2.4f + -1.2 + -2.4f

Combine like terms: 4.8f + -2.4f = 2.4f
-1.2 + 2.4f + 1.2f2 = 1.2 + 2.4f + -1.2 + -2.4f

Reorder the terms:
-1.2 + 2.4f + 1.2f2 = 1.2 + -1.2 + 2.4f + -2.4f

Combine like terms: 1.2 + -1.2 = 0.0
-1.2 + 2.4f + 1.2f2 = 0.0 + 2.4f + -2.4f
-1.2 + 2.4f + 1.2f2 = 2.4f + -2.4f

Combine like terms: 2.4f + -2.4f = 0.0
-1.2 + 2.4f + 1.2f2 = 0.0

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

Divide each side by '1.2'.
-1 + 2f + f2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2f + 1 + f2 = 0 + 1

Reorder the terms:
-1 + 1 + 2f + f2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2f + f2 = 0 + 1
2f + f2 = 0 + 1

Combine like terms: 0 + 1 = 1
2f + f2 = 1

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 = 1 + 1

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

Combine like terms: 1 + 1 = 2
1 + 2f + f2 = 2

Factor a perfect square on the left side:
(f + 1)(f + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(f + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
f + 1 = 1.414213562

Simplifying
f + 1 = 1.414213562

Reorder the terms:
1 + f = 1.414213562

Solving
1 + f = 1.414213562

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 = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + f = 1.414213562 + -1
f = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
f = 0.414213562

Simplifying
f = 0.414213562

Subproblem 2
f + 1 = -1.414213562

Simplifying
f + 1 = -1.414213562

Reorder the terms:
1 + f = -1.414213562

Solving
1 + f = -1.414213562

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 = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + f = -1.414213562 + -1
f = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
f = -2.414213562

Simplifying
f = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {0.414213562, -2.414213562}