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

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

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

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

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

Solving
8f + -4f2 = -8 + -4f

Solving for variable 'f'.

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

Combine like terms: 8f + 4f = 12f
8 + 12f + -4f2 = -8 + -4f + 8 + 4f

Reorder the terms:
8 + 12f + -4f2 = -8 + 8 + -4f + 4f

Combine like terms: -8 + 8 = 0
8 + 12f + -4f2 = 0 + -4f + 4f
8 + 12f + -4f2 = -4f + 4f

Combine like terms: -4f + 4f = 0
8 + 12f + -4f2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + 3f + -1f2) = 0

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

Simplifying
2 + 3f + -1f2 = 0

Solving
2 + 3f + -1f2 = 0

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

Divide each side by '-1'.
-2 + -3f + f2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -3f + 2 + f2 = 0 + 2

Reorder the terms:
-2 + 2 + -3f + f2 = 0 + 2

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

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

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 = 2 + 2.25

Reorder the terms:
2.25 + -3f + f2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + -3f + f2 = 4.25

Factor a perfect square on the left side:
(f + -1.5)(f + -1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(f + -1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1
f + -1.5 = 2.061552813

Simplifying
f + -1.5 = 2.061552813

Reorder the terms:
-1.5 + f = 2.061552813

Solving
-1.5 + f = 2.061552813

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 = 2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + f = 2.061552813 + 1.5
f = 2.061552813 + 1.5

Combine like terms: 2.061552813 + 1.5 = 3.561552813
f = 3.561552813

Simplifying
f = 3.561552813

Subproblem 2
f + -1.5 = -2.061552813

Simplifying
f + -1.5 = -2.061552813

Reorder the terms:
-1.5 + f = -2.061552813

Solving
-1.5 + f = -2.061552813

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 = -2.061552813 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + f = -2.061552813 + 1.5
f = -2.061552813 + 1.5

Combine like terms: -2.061552813 + 1.5 = -0.561552813
f = -0.561552813

Simplifying
f = -0.561552813

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {3.561552813, -0.561552813}
Solution
f = {3.561552813, -0.561552813}