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

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


Simplifying
-2f(2f + -4) = -4(-1f + 2)

Reorder the terms:
-2f(-4 + 2f) = -4(-1f + 2)
(-4 * -2f + 2f * -2f) = -4(-1f + 2)
(8f + -4f2) = -4(-1f + 2)

Reorder the terms:
8f + -4f2 = -4(2 + -1f)
8f + -4f2 = (2 * -4 + -1f * -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 = 4f
8 + 4f + -4f2 = -8 + 4f + 8 + -4f

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

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

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

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

Factor a trinomial.
4((2 + -1f)(1 + f)) = 0

Ignore the factor 4.

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

Simplifying
2 + -1f = 0

Solving
2 + -1f = 0

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

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

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

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

Divide each side by '-1'.
f = 2

Simplifying
f = 2

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

Simplifying
1 + f = 0

Solving
1 + f = 0

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 = 0 + -1

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

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

Simplifying
f = -1
Solution
f = {2, -1}

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