f(x)=10x-2x^2f(x)

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Solution for f(x)=10x-2x^2f(x) equation: 


Simplifying
f(x) = 10x + -2x2f(x)

Multiply f * x
fx = 10x + -2x2f(x)

Multiply fx2 * x
fx = 10x + -2fx3

Reorder the terms:
fx = -2fx3 + 10x

Solving
fx = -2fx3 + 10x

Solving for variable 'f'.

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

Add '2fx3' to each side of the equation.
fx + 2fx3 = -2fx3 + 2fx3 + 10x

Combine like terms: -2fx3 + 2fx3 = 0
fx + 2fx3 = 0 + 10x
fx + 2fx3 = 10x

Combine like terms: 10x + -10x = 0
fx + 2fx3 + -10x = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(f + 2fx2 + -10) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

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 '(f + 2fx2 + -10)' equal to zero and attempt to solve:

Simplifying
f + 2fx2 + -10 = 0

Reorder the terms:
-10 + f + 2fx2 = 0

Solving
-10 + f + 2fx2 = 0

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

Add '10' to each side of the equation.
-10 + f + 10 + 2fx2 = 0 + 10

Reorder the terms:
-10 + 10 + f + 2fx2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + f + 2fx2 = 0 + 10
f + 2fx2 = 0 + 10

Combine like terms: 0 + 10 = 10
f + 2fx2 = 10

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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