(7sf-8s^2f+13sf^2)-(8sf^2-3sf-13s^2f)=

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Solution for (7sf-8s^2f+13sf^2)-(8sf^2-3sf-13s^2f)= equation: 


Simplifying
(7sf + -8s2f + 13sf2) + -1(8sf2 + -3sf + -13s2f) = 0

Remove parenthesis around (7fs + -8fs2 + 13f2s)
7fs + -8fs2 + 13f2s + -1(8sf2 + -3sf + -13s2f) = 0

Reorder the terms:
7fs + -8fs2 + 13f2s + -1(-3fs + -13fs2 + 8f2s) = 0
7fs + -8fs2 + 13f2s + (-3fs * -1 + -13fs2 * -1 + 8f2s * -1) = 0
7fs + -8fs2 + 13f2s + (3fs + 13fs2 + -8f2s) = 0

Reorder the terms:
7fs + 3fs + -8fs2 + 13fs2 + 13f2s + -8f2s = 0

Combine like terms: 7fs + 3fs = 10fs
10fs + -8fs2 + 13fs2 + 13f2s + -8f2s = 0

Combine like terms: -8fs2 + 13fs2 = 5fs2
10fs + 5fs2 + 13f2s + -8f2s = 0

Combine like terms: 13f2s + -8f2s = 5f2s
10fs + 5fs2 + 5f2s = 0

Solving
10fs + 5fs2 + 5f2s = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '5fs'.
5fs(2 + s + f) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'fs' equal to zero and attempt to solve:

Simplifying
fs = 0

Solving
fs = 0

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

Simplifying
fs = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
2 + s + f = 0

Reorder the terms:
2 + f + s = 0

Solving
2 + f + s = 0

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

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

Reorder the terms:
2 + -2 + f + s = 0 + -2

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

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

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

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

Simplifying
f = -2 + -1s
Solution
f = {-2 + -1s}

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