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

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


Simplifying
f2 + -1(4f + -2f2 + -8) = 2f2 + 4f + -8

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

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

Combine like terms: f2 + 2f2 = 3f2
8 + -4f + 3f2 = 2f2 + 4f + -8

Reorder the terms:
8 + -4f + 3f2 = -8 + 4f + 2f2

Solving
8 + -4f + 3f2 = -8 + 4f + 2f2

Solving for variable 'f'.

Reorder the terms:
8 + 8 + -4f + -4f + 3f2 + -2f2 = -8 + 4f + 2f2 + 8 + -4f + -2f2

Combine like terms: 8 + 8 = 16
16 + -4f + -4f + 3f2 + -2f2 = -8 + 4f + 2f2 + 8 + -4f + -2f2

Combine like terms: -4f + -4f = -8f
16 + -8f + 3f2 + -2f2 = -8 + 4f + 2f2 + 8 + -4f + -2f2

Combine like terms: 3f2 + -2f2 = 1f2
16 + -8f + 1f2 = -8 + 4f + 2f2 + 8 + -4f + -2f2

Reorder the terms:
16 + -8f + 1f2 = -8 + 8 + 4f + -4f + 2f2 + -2f2

Combine like terms: -8 + 8 = 0
16 + -8f + 1f2 = 0 + 4f + -4f + 2f2 + -2f2
16 + -8f + 1f2 = 4f + -4f + 2f2 + -2f2

Combine like terms: 4f + -4f = 0
16 + -8f + 1f2 = 0 + 2f2 + -2f2
16 + -8f + 1f2 = 2f2 + -2f2

Combine like terms: 2f2 + -2f2 = 0
16 + -8f + 1f2 = 0

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


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

Simplifying
4 + -1f = 0

Solving
4 + -1f = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1f = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1f = 0 + -4
-1f = 0 + -4

Combine like terms: 0 + -4 = -4
-1f = -4

Divide each side by '-1'.
f = 4

Simplifying
f = 4

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

Simplifying
4 + -1f = 0

Solving
4 + -1f = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1f = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1f = 0 + -4
-1f = 0 + -4

Combine like terms: 0 + -4 = -4
-1f = -4

Divide each side by '-1'.
f = 4

Simplifying
f = 4
Solution
f = {4, 4}

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