$$ 2((x)(2(x-5))+(2(x-5))(x-5)+(x-5)(x)=48 $$

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Solve the equation $$ 2((x)(2(x-5))+(2(x-5))(x-5)+(x-5)(x))=48 $$.
Solve the quadratic equation by following steps:
- step0: Solve using the quadratic formula:
  $$2\left(x\left(2\left(x-5ight)ight)+\left(2\left(x-5ight)ight)\left(x-5ight)+\left(x-5ight)xight)=48$$
- step1: Remove the parentheses:
  $$2\left(x	imes 2\left(x-5ight)+2\left(x-5ight)\left(x-5ight)+\left(x-5ight)xight)=48$$
- step2: Simplify:
  $$2\left(5x^{2}-35x+50ight)=48$$
- step3: Expand the expression:
  $$10x^{2}-70x+100=48$$
- step4: Move the expression to the left side:
  $$10x^{2}-70x+52=0$$
- step5: Solve using the quadratic formula:
  $$x=\frac{70\pm \sqrt{\left(-70ight)^{2}-4	imes 10	imes 52}}{2	imes 10}$$
- step6: Simplify the expression:
  $$x=\frac{70\pm \sqrt{\left(-70ight)^{2}-4	imes 10	imes 52}}{20}$$
- step7: Simplify the expression:
  $$x=\frac{70\pm \sqrt{2820}}{20}$$
- step8: Simplify the expression:
  $$x=\frac{70\pm 2\sqrt{705}}{20}$$
- step9: Separate into possible cases:
  $$\begin{align}&x=\frac{70+2\sqrt{705}}{20}\&x=\frac{70-2\sqrt{705}}{20}\end{align}$$
- step10: Simplify the expression:
  $$\begin{align}&x=\frac{35+\sqrt{705}}{10}\&x=\frac{70-2\sqrt{705}}{20}\end{align}$$
- step11: Simplify the expression:
  $$\begin{align}&x=\frac{35+\sqrt{705}}{10}\&x=\frac{35-\sqrt{705}}{10}\end{align}$$
- step12: Rewrite:
  $$x_{1}=\frac{35-\sqrt{705}}{10},x_{2}=\frac{35+\sqrt{705}}{10}$$
The solutions to the equation $$2((x)(2(x-5))+(2(x-5))(x-5)+(x-5)(x))=48$$ are $$x_{1}=\frac{35-\sqrt{705}}{10}$$ and $$x_{2}=\frac{35+\sqrt{705}}{10}$$.
The solutions are $$ x = \frac{35 - \sqrt{705}}{10} $$ and $$ x = \frac{35 + \sqrt{705}}{10} $$.

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