The following calculator can be used to solve polynomial equations. These are equations of 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 $(2x^23x5=0)$,
3. Cubic equation $(5x^3 + 2x^2  3x + 1 = 0)$ . . .
How to use this calculator?
Example 1: to solve (2x + 3)^{2}  4(x + 1)^{2} = 1 type (2x + 3)^2  4(x + 1)^2 = 1.
Example 2: to solve $\frac{3x^21}{2}+\frac{2x+1}{3} = \frac{x^22}{4} + \frac{1}{3}$ type (3x^2  1)/2 + (2x + 1)/3 = (x^2  2)/4 + 1/3.

We use 4 steps to solve a polynomial equation in one variable. The following example uses all four steps but some equations may not require all of them.
Example:
Solve $\frac{3x^21}{2}+\frac{2x+1}{3} = \frac{x^22}{4} + \frac{1}{3}$
Solution:
Step 1: Eliminate fractions by multiplying each side by the least common denominator.
In this example we multiply both sides by 12.
$$ \begin{aligned} \frac{3x^21}{2}+\frac{2x+1}{3} & = \frac{x^22}{4} + \frac{1}{3} \\ {\color{red}{12}}\cdot\frac{3x^21}{2}+{\color{red}{12}}\cdot\frac{2x+1}{3} & = {\color{red}{12}}\cdot\frac{x^22}{4} + {\color{red}{12}}\cdot\frac{1}{3}\\ 6\cdot(3x^21)+4\cdot(2x+1) & = 3\cdot(x^22) + 4 \end{aligned} $$Step 2:Simplify each side by clearing parentheses and combining like terms.
$$ \begin{aligned} 6\cdot(3x^21)+4\cdot(2x+1) & = 3\cdot(x^22) + 4 \\ 18x^26+8x+4 & = 3x^26+4\\ 18x^2+8x2 & = 3x^22\\ \end{aligned} $$Step 3:Use the addition property to get all terms on one side of the equation.
$$ \begin{aligned} 18x^2+8x2 & = {\color{red}{3x^22}}\\ 18x^2+8x2{\color{red}{3x^2+2}} & = 0\\ 15x^2+8x & = 0 \end{aligned} $$Step 4:Finally, solve the equation.
Here we have second degree equation so you can use stepbystep quadratic equation solver to find the solutions:
$$ {\color{blue}{ x_1 = 0, x_2 = \frac{8}{15} }} $$If you have an equation of higher degree then you can use polynomial roots calculator.
Unfortunately, this calculator will show you the solution, but without explanation.
Please tell me how can I make this better.
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