Polynomial equation solver

This calculator solves equations in the form $P(x)=Q(x)$, where $P(x)$ and $Q(x)$ are polynomials. Special cases of such equations are:

1. Linear equation: $ 2x + 1 = 3 $.

2. Quadratic Equation: $ (2x + 1)^2 - (x - 1)^2 = \frac{1}{2}$

3. Cubic equation: $ 5x^3 + 2x^2 - 3x + 1 = \frac{1}{3} x $

Polynomial Equation Solver
To solve $(2x + 3)^2 - \frac{4}{3}(x + 1)^2 = \frac{3}{2}$ type (2x+3)^2-4/3(x+1)^2=3/2.
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examples
example 1:ex 1:
$$\frac{x}{2} \left(x^2 + 1\right) = 2(x+1)^2 - 5x - 3$$
example 2:ex 2:
$$\frac{3x^2-1}{2} + \frac{2x+1}{3} = \frac{x^2-2}{4} + \frac{1}{3}$$
example 3:ex 3:
$$(x^3-1)^2 - (x^2-1)^2 = x - 1$$

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