f(x)=3x^2-2x^2f(x-1)

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Solution for f(x)=3x^2-2x^2f(x-1) equation: 


Simplifying
f(x) = 3x2 + -2x2f(x + -1)

Multiply f * x
fx = 3x2 + -2x2f(x + -1)

Reorder the terms:
fx = 3x2 + -2fx2(-1 + x)
fx = 3x2 + (-1 * -2fx2 + x * -2fx2)
fx = 3x2 + (2fx2 + -2fx3)

Reorder the terms:
fx = 2fx2 + -2fx3 + 3x2

Solving
fx = 2fx2 + -2fx3 + 3x2

Solving for variable 'f'.

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

Add '-2fx2' to each side of the equation.
fx + -2fx2 = 2fx2 + -2fx3 + -2fx2 + 3x2

Reorder the terms:
fx + -2fx2 = 2fx2 + -2fx2 + -2fx3 + 3x2

Combine like terms: 2fx2 + -2fx2 = 0
fx + -2fx2 = 0 + -2fx3 + 3x2
fx + -2fx2 = -2fx3 + 3x2

Add '2fx3' to each side of the equation.
fx + -2fx2 + 2fx3 = -2fx3 + 2fx3 + 3x2

Combine like terms: -2fx3 + 2fx3 = 0
fx + -2fx2 + 2fx3 = 0 + 3x2
fx + -2fx2 + 2fx3 = 3x2

Combine like terms: 3x2 + -3x2 = 0
fx + -2fx2 + 2fx3 + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(f + -2fx + 2fx2 + -3x) = 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 + -2fx + 2fx2 + -3x)' equal to zero and attempt to solve:

Simplifying
f + -2fx + 2fx2 + -3x = 0

Solving
f + -2fx + 2fx2 + -3x = 0

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

Add '3x' to each side of the equation.
f + -2fx + 2fx2 + -3x + 3x = 0 + 3x

Combine like terms: -3x + 3x = 0
f + -2fx + 2fx2 + 0 = 0 + 3x
f + -2fx + 2fx2 = 0 + 3x
Remove the zero:
f + -2fx + 2fx2 = 3x

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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