Solve the indicial equation 2 (2x+1)=27(x−1)

$$3(2x) + 3(1) = 27(x) - 27(1)$$ $$6x + 3 = 27x - 27$$

Subtract $27x$ from both sides:

$$6x - 27x + 3 = -27$$

Subtract 3 from both sides:

$$6x - 27x = -27 - 3$$

$$x = \frac{-30}{-21}$$ $$x = \frac{30}{21}$$

Divide both the numerator and the denominator by their greatest common divisor, which is 3:

$$x = \frac{30 \div 3}{21 \div 3}$$ $$x = \frac{10}{7}$$

As a decimal, rounded to four decimal places:

$$x \approx 1.4286$$

The solution to the equation is $\boxed*{x = \frac{10}{7} \approx 1.4286}$.