Solve for a
\left\{\begin{matrix}a=-\frac{i\left(2x+3\right)\left(1-x\right)^{2}}{ry}\text{, }&y\neq 0\text{ and }r\neq 0\\a\in \mathrm{C}\text{, }&\left(x=1\text{ and }r=0\right)\text{ or }\left(x=1\text{ and }y=0\right)\text{ or }\left(x=-\frac{3}{2}\text{ and }r=0\right)\text{ or }\left(x=-\frac{3}{2}\text{ and }y=0\right)\end{matrix}\right.
Solve for r
\left\{\begin{matrix}r=-\frac{i\left(2x+3\right)\left(1-x\right)^{2}}{ay}\text{, }&y\neq 0\text{ and }a\neq 0\\r\in \mathrm{C}\text{, }&\left(x=1\text{ and }a=0\right)\text{ or }\left(x=1\text{ and }y=0\right)\text{ or }\left(x=-\frac{3}{2}\text{ and }a=0\right)\text{ or }\left(x=-\frac{3}{2}\text{ and }y=0\right)\end{matrix}\right.
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ariy=\left(1-2x+x^{2}\right)\left(2x+3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x\right)^{2}.
ariy=-4x+3-x^{2}+2x^{3}
Use the distributive property to multiply 1-2x+x^{2} by 2x+3 and combine like terms.
irya=2x^{3}-x^{2}-4x+3
The equation is in standard form.
\frac{irya}{iry}=\frac{\left(2x+3\right)\left(x-1\right)^{2}}{iry}
Divide both sides by iry.
a=\frac{\left(2x+3\right)\left(x-1\right)^{2}}{iry}
Dividing by iry undoes the multiplication by iry.
a=-\frac{i\left(2x+3\right)\left(x-1\right)^{2}}{ry}
Divide \left(3+2x\right)\left(-1+x\right)^{2} by iry.
ariy=\left(1-2x+x^{2}\right)\left(2x+3\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-x\right)^{2}.
ariy=-4x+3-x^{2}+2x^{3}
Use the distributive property to multiply 1-2x+x^{2} by 2x+3 and combine like terms.
iayr=2x^{3}-x^{2}-4x+3
The equation is in standard form.
\frac{iayr}{iay}=\frac{\left(2x+3\right)\left(x-1\right)^{2}}{iay}
Divide both sides by iay.
r=\frac{\left(2x+3\right)\left(x-1\right)^{2}}{iay}
Dividing by iay undoes the multiplication by iay.
r=-\frac{i\left(2x+3\right)\left(x-1\right)^{2}}{ay}
Divide \left(3+2x\right)\left(-1+x\right)^{2} by iay.
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