-4f(f-2)-2f=-8

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Solution for -4f(f-2)-2f=-8 equation:


Simplifying
-4f(f + -2) + -2f = -8

Reorder the terms:
-4f(-2 + f) + -2f = -8
(-2 * -4f + f * -4f) + -2f = -8
(8f + -4f2) + -2f = -8

Reorder the terms:
8f + -2f + -4f2 = -8

Combine like terms: 8f + -2f = 6f
6f + -4f2 = -8

Solving
6f + -4f2 = -8

Solving for variable 'f'.

Reorder the terms:
8 + 6f + -4f2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 6f + -4f2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 3f + -2f2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 3f + -2f2)' equal to zero and attempt to solve:

Simplifying
4 + 3f + -2f2 = 0

Solving
4 + 3f + -2f2 = 0

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

Divide each side by '-2'.
-2 + -1.5f + f2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -1.5f + 2 + f2 = 0 + 2

Reorder the terms:
-2 + 2 + -1.5f + f2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1.5f + f2 = 0 + 2
-1.5f + f2 = 0 + 2

Combine like terms: 0 + 2 = 2
-1.5f + f2 = 2

The f term is -1.5f.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5f + 0.5625 + f2 = 2 + 0.5625

Reorder the terms:
0.5625 + -1.5f + f2 = 2 + 0.5625

Combine like terms: 2 + 0.5625 = 2.5625
0.5625 + -1.5f + f2 = 2.5625

Factor a perfect square on the left side:
(f + -0.75)(f + -0.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(f + -0.75) equal to 1.600781059 and -1.600781059.


Subproblem 1
f + -0.75 = 1.600781059

Simplifying
f + -0.75 = 1.600781059

Reorder the terms:
-0.75 + f = 1.600781059

Solving
-0.75 + f = 1.600781059

Solving for variable 'f'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + f = 1.600781059 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + f = 1.600781059 + 0.75
f = 1.600781059 + 0.75

Combine like terms: 1.600781059 + 0.75 = 2.350781059
f = 2.350781059

Simplifying
f = 2.350781059


Subproblem 2
f + -0.75 = -1.600781059

Simplifying
f + -0.75 = -1.600781059

Reorder the terms:
-0.75 + f = -1.600781059

Solving
-0.75 + f = -1.600781059

Solving for variable 'f'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + f = -1.600781059 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + f = -1.600781059 + 0.75
f = -1.600781059 + 0.75

Combine like terms: -1.600781059 + 0.75 = -0.850781059
f = -0.850781059

Simplifying
f = -0.850781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {2.350781059, -0.850781059}
Solution
f = {2.350781059, -0.850781059}

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