f+f(f-6)=57-(17-f^2)

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Solution for f+f(f-6)=57-(17-f^2) equation: 


Simplifying
f + f(f + -6) = 57 + -1(17 + -1f2)

Reorder the terms:
f + f(-6 + f) = 57 + -1(17 + -1f2)
f + (-6 * f + f * f) = 57 + -1(17 + -1f2)
f + (-6f + f2) = 57 + -1(17 + -1f2)

Combine like terms: f + -6f = -5f
-5f + f2 = 57 + -1(17 + -1f2)
-5f + f2 = 57 + (17 * -1 + -1f2 * -1)
-5f + f2 = 57 + (-17 + 1f2)

Combine like terms: 57 + -17 = 40
-5f + f2 = 40 + 1f2

Solving
-5f + f2 = 40 + 1f2

Solving for variable 'f'.

Reorder the terms:
-40 + -5f + f2 + -1f2 = 40 + 1f2 + -40 + -1f2

Combine like terms: f2 + -1f2 = 0
-40 + -5f + 0 = 40 + 1f2 + -40 + -1f2
-40 + -5f = 40 + 1f2 + -40 + -1f2

Reorder the terms:
-40 + -5f = 40 + -40 + 1f2 + -1f2

Combine like terms: 40 + -40 = 0
-40 + -5f = 0 + 1f2 + -1f2
-40 + -5f = 1f2 + -1f2

Combine like terms: 1f2 + -1f2 = 0
-40 + -5f = 0

Factor out the Greatest Common Factor (GCF), '-5'.
-5(8 + f) = 0

Ignore the factor -5.

Subproblem 1
Set the factor '(8 + f)' equal to zero and attempt to solve:

Simplifying
8 + f = 0

Solving
8 + f = 0

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

Add '-8' to each side of the equation.
8 + -8 + f = 0 + -8

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

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

Simplifying
f = -8
Solution
f = {-8}

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