Solve each of the following equations and also check your result in each case: `6. 5 x+(19. 5 x-32. 5)/2=6. 5 x+13+((13 x-26)/2)` `(3x-8)(3x+2)-\ (4x-11)\ (2x+1)=(x-3)x+7)` `[(2x+3)+(x+5)]^2+[(2x+3)-(x+5)]^2=10 x^2+92`

Explanation

Let's solve the equations step by step.

### Equation 1:
**Given:**
\[ 5x + \frac{19.5x - 32.5}{2} = 6.5x + 13 + \frac{13x - 26}{2} \]

**Step 1:** Eliminate \(6.5x\) from both sides.
\[
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