Solve y^prime=6x(x+1)(x-2)*A

$$y ^ { \prime } = 6 x ( x + 1 ) ( x - 2 ) \cdot A$$

Solve for A

$$\left\{\begin{matrix}\\A=0\text{, }&\text{unconditionally}\\A\in \mathrm{R}\text{, }&x=2\text{ or }x=-1\text{ or }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6x by x+1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(6x^{2}+6x\right)\left(x-2\right)A$$

Use the distributive property to multiply 6x^{2}+6x by x-2 and combine like terms.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=\left(6x^{3}-6x^{2}-12x\right)A$$

Use the distributive property to multiply 6x^{3}-6x^{2}-12x by A.

$$\frac{\mathrm{d}}{\mathrm{d}x}(y)=6x^{3}A-6x^{2}A-12xA$$

Swap sides so that all variable terms are on the left hand side.

$$6x^{3}A-6x^{2}A-12xA=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

Combine all terms containing A.

$$\left(6x^{3}-6x^{2}-12x\right)A=\frac{\mathrm{d}}{\mathrm{d}x}(y)$$

The equation is in standard form.

$$\left(6x^{3}-6x^{2}-12x\right)A=0$$

Divide 0 by 6x^{3}-6x^{2}-12x.

$$A=0$$

Solve for x

$$\left\{\begin{matrix}\\x=-1\text{; }x=0\text{; }x=2\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&A=0\end{matrix}\right.$$