Solve the equation
13. 9^3c + 1 = 27^3c - 1​

Simplifying
9(3c + -1) = 27(3c + -1)

Reorder the terms:
9(-1 + 3c) = 27(3c + -1)
(-1 * 9 + 3c * 9) = 27(3c + -1)
(-9 + 27c) = 27(3c + -1)

Reorder the terms:
-9 + 27c = 27(-1 + 3c)
-9 + 27c = (-1 * 27 + 3c * 27)
-9 + 27c = (-27 + 81c)

Solving
-9 + 27c = -27 + 81c

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-81c' to each side of the equation.
-9 + 27c + -81c = -27 + 81c + -81c

Combine like terms: 27c + -81c = -54c
-9 + -54c = -27 + 81c + -81c

Combine like terms: 81c + -81c = 0
-9 + -54c = -27 + 0
-9 + -54c = -27

Add '9' to each side of the equation.
-9 + 9 + -54c = -27 + 9

Combine like terms: -9 + 9 = 0
0 + -54c = -27 + 9
-54c = -27 + 9

Combine like terms: -27 + 9 = -18
-54c = -18

Divide each side by '-54'.
c = 0.3333333333

Simplifying
c = 0.3333333333