-5f(f+2)=3f+2

Solution for -5f(f+2)=3f+2 equation:

Simplifying
-5f(f + 2) = 3f + 2

Reorder the terms:
-5f(2 + f) = 3f + 2
(2 * -5f + f * -5f) = 3f + 2
(-10f + -5f2) = 3f + 2

Reorder the terms:
-10f + -5f2 = 2 + 3f

Solving
-10f + -5f2 = 2 + 3f

Solving for variable 'f'.

Reorder the terms:
-2 + -10f + -3f + -5f2 = 2 + 3f + -2 + -3f

Combine like terms: -10f + -3f = -13f
-2 + -13f + -5f2 = 2 + 3f + -2 + -3f

Reorder the terms:
-2 + -13f + -5f2 = 2 + -2 + 3f + -3f

Combine like terms: 2 + -2 = 0
-2 + -13f + -5f2 = 0 + 3f + -3f
-2 + -13f + -5f2 = 3f + -3f

Combine like terms: 3f + -3f = 0
-2 + -13f + -5f2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 13f + 5f2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 13f + 5f2)' equal to zero and attempt to solve:

Simplifying
2 + 13f + 5f2 = 0

Solving
2 + 13f + 5f2 = 0

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

Divide each side by '5'.
0.4 + 2.6f + f2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 2.6f + -0.4 + f2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 2.6f + f2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 2.6f + f2 = 0 + -0.4
2.6f + f2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
2.6f + f2 = -0.4

The f term is 2.6f.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6f + 1.69 + f2 = -0.4 + 1.69

Reorder the terms:
1.69 + 2.6f + f2 = -0.4 + 1.69

Combine like terms: -0.4 + 1.69 = 1.29
1.69 + 2.6f + f2 = 1.29

Factor a perfect square on the left side:
(f + 1.3)(f + 1.3) = 1.29

Calculate the square root of the right side: 1.135781669

Break this problem into two subproblems by setting 
(f + 1.3) equal to 1.135781669 and -1.135781669.

Subproblem 1
f + 1.3 = 1.135781669

Simplifying
f + 1.3 = 1.135781669

Reorder the terms:
1.3 + f = 1.135781669

Solving
1.3 + f = 1.135781669

Solving for variable 'f'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + f = 1.135781669 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + f = 1.135781669 + -1.3
f = 1.135781669 + -1.3

Combine like terms: 1.135781669 + -1.3 = -0.164218331
f = -0.164218331

Simplifying
f = -0.164218331

Subproblem 2
f + 1.3 = -1.135781669

Simplifying
f + 1.3 = -1.135781669

Reorder the terms:
1.3 + f = -1.135781669

Solving
1.3 + f = -1.135781669

Solving for variable 'f'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + f = -1.135781669 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + f = -1.135781669 + -1.3
f = -1.135781669 + -1.3

Combine like terms: -1.135781669 + -1.3 = -2.435781669
f = -2.435781669

Simplifying
f = -2.435781669

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {-0.164218331, -2.435781669}
Solution
f = {-0.164218331, -2.435781669}