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

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


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

Reorder the terms:
f(-1 + 2x) = 2x + -3x2f(3x + 2)
(-1 * f + 2x * f) = 2x + -3x2f(3x + 2)
(-1f + 2fx) = 2x + -3x2f(3x + 2)

Reorder the terms:
-1f + 2fx = 2x + -3fx2(2 + 3x)
-1f + 2fx = 2x + (2 * -3fx2 + 3x * -3fx2)
-1f + 2fx = 2x + (-6fx2 + -9fx3)

Reorder the terms:
-1f + 2fx = -6fx2 + -9fx3 + 2x

Solving
-1f + 2fx = -6fx2 + -9fx3 + 2x

Solving for variable 'f'.

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

Add '6fx2' to each side of the equation.
-1f + 2fx + 6fx2 = -6fx2 + -9fx3 + 6fx2 + 2x

Reorder the terms:
-1f + 2fx + 6fx2 = -6fx2 + 6fx2 + -9fx3 + 2x

Combine like terms: -6fx2 + 6fx2 = 0
-1f + 2fx + 6fx2 = 0 + -9fx3 + 2x
-1f + 2fx + 6fx2 = -9fx3 + 2x

Add '9fx3' to each side of the equation.
-1f + 2fx + 6fx2 + 9fx3 = -9fx3 + 9fx3 + 2x

Combine like terms: -9fx3 + 9fx3 = 0
-1f + 2fx + 6fx2 + 9fx3 = 0 + 2x
-1f + 2fx + 6fx2 + 9fx3 = 2x

Combine like terms: 2x + -2x = 0
-1f + 2fx + 6fx2 + 9fx3 + -2x = 0

The solution to this equation could not be determined.

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