|2-x||x-7|=36

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$$\begin{gathered} \left|2-\mathrm{x}\right|\left|\mathrm{x}-7\right|=36 \\ \Rightarrow \left|-\left(\mathrm{x}-2\right)\right|\left|\mathrm{x}-7\right|=36 \\ \mathrm{Now} \left|-\left(\mathrm{x}-2\right)\right|=\left|\left(\mathrm{x}-2\right)\right| \\ \Rightarrow \left|\mathrm{x}-2\right|\left|\mathrm{x}-7\right|=36 \\ \mathrm{We} \mathrm{know} \mathrm{that} \left|\mathrm{a}\right|\left|\mathrm{b}\right|=\left|\mathrm{ab}\right| \\ \Rightarrow \left|\left(\mathrm{x}-2\right)\left(\mathrm{x}-7\right)\right|=36 \\ \Rightarrow \left|{\mathrm{x}}^2-7\mathrm{x}-2\mathrm{x}+14\right|=36 \\ \Rightarrow \left|{\mathrm{x}}^2-9\mathrm{x}+14\right|=36 \\ \mathrm{We} \mathrm{know} \mathrm{that} \left|-2\right|=2 \mathrm{and} \left|2\right|=2 \\ \Rightarrow \mathrm{If} \left|\mathrm{x}\right|=\mathrm{a} ,\mathrm{where} \mathrm{a}>0 \\ \Rightarrow \mathrm{x}=\pm \mathrm{a} \\ \Rightarrow {\mathrm{x}}^2-9\mathrm{x}+14=\pm 36 \\ \mathrm{When} {\mathrm{x}}^2-9\mathrm{x}+14=36 \\ \Rightarrow {\mathrm{x}}^2-9\mathrm{x}+14-36=0 \\ \Rightarrow {\mathrm{x}}^2-9\mathrm{x}-22=0 \\ \Rightarrow {\mathrm{x}}^2+2\mathrm{x}-11\mathrm{x}-22=0 \\ \Rightarrow \mathrm{x}\left(\mathrm{x}+2\right)-11\left(\mathrm{x}+2\right)=0 \\ \Rightarrow \left(\mathrm{x}-11\right)\left(\mathrm{x}+2\right)=0 \\ \mathbf{\Rightarrow }{\mathbf{x}}_{\mathbf{1}}\mathbf{=}\mathbf{11} \\ \mathbf{\Rightarrow }{\mathbf{x}}_{\mathbf{2}}\mathbf{=}\mathbf{-}\mathbf{2} \\ \mathrm{When} {\mathrm{x}}^2-9\mathrm{x}+14=-36 \\ \Rightarrow {\mathrm{x}}^2-9\mathrm{x}+14+36=0 \\ \Rightarrow {\mathrm{x}}^2-9\mathrm{x}+50=0 \\ \mathrm{Discriminant}={\left(-9\right)}^2-4\times 1\times 50=81-200 \\ \Rightarrow \mathrm{Discriminant}=-119<0 \\ \Rightarrow {\mathrm{x}}^2-9\mathrm{x}+50=0 \mathrm{will} \mathrm{have} \mathrm{no} \mathrm{solution}. \\ \mathbf{Hence}\mathbf{ }\mathbf{solutions}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{ }\left|\mathbf{2}\mathbf{-}\mathbf{x}\right|\left|\mathbf{x}\mathbf{-}\mathbf{7}\right|\mathbf{=}\mathbf{36}\mathbf{ }\mathbf{are}\mathbf{ }\mathbf{x}\mathbf{=}\mathbf{11}\mathbf{ }\mathbf{and}\mathbf{ }\mathbf{x}\mathbf{=}\mathbf{-}\mathbf{2}\mathbf{.} \end{gathered}$$

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