Solve for x and simplify the answer fully. $$ \frac{x-8}{x+6}=\frac{3}{5} $$

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Solve the equation $$ \frac{x-8}{x+6}=\frac{3}{5} $$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{x-8}{x+6}=\frac{3}{5}$$
- step1: Find the domain:
  $$\frac{x-8}{x+6}=\frac{3}{5},x
eq -6$$
- step2: Cross multiply:
  $$\left(x-8ight)	imes 5=\left(x+6ight)	imes 3$$
- step3: Simplify the equation:
  $$5\left(x-8ight)=3\left(x+6ight)$$
- step4: Calculate:
  $$5x-40=3\left(x+6ight)$$
- step5: Calculate:
  $$5x-40=3x+18$$
- step6: Move the expression to the left side:
  $$5x-40-\left(3x+18ight)=0$$
- step7: Calculate:
  $$2x-58=0$$
- step8: Move the constant to the right side:
  $$2x=0+58$$
- step9: Remove 0:
  $$2x=58$$
- step10: Divide both sides:
  $$\frac{2x}{2}=\frac{58}{2}$$
- step11: Divide the numbers:
  $$x=29$$
- step12: Check if the solution is in the defined range:
  $$x=29,x
eq -6$$
- step13: Find the intersection:
  $$x=29$$
The solution to the equation $$\frac{x-8}{x+6}=\frac{3}{5}$$ is $$x=29$$.
$$ x=29 $$

Solve for x and simplify the answer fully.

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