3(3n+2)=7(8n+7)+1

Solution for 3(3n+2)=7(8n+7)+1 equation:

Simplifying
3(3n + 2) = 7(8n + 7) + 1

Reorder the terms:
3(2 + 3n) = 7(8n + 7) + 1
(2 * 3 + 3n * 3) = 7(8n + 7) + 1
(6 + 9n) = 7(8n + 7) + 1

Reorder the terms:
6 + 9n = 7(7 + 8n) + 1
6 + 9n = (7 * 7 + 8n * 7) + 1
6 + 9n = (49 + 56n) + 1

Reorder the terms:
6 + 9n = 49 + 1 + 56n

Combine like terms: 49 + 1 = 50
6 + 9n = 50 + 56n

Solving
6 + 9n = 50 + 56n

Solving for variable 'n'.

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

Add '-56n' to each side of the equation.
6 + 9n + -56n = 50 + 56n + -56n

Combine like terms: 9n + -56n = -47n
6 + -47n = 50 + 56n + -56n

Combine like terms: 56n + -56n = 0
6 + -47n = 50 + 0
6 + -47n = 50

Add '-6' to each side of the equation.
6 + -6 + -47n = 50 + -6

Combine like terms: 6 + -6 = 0
0 + -47n = 50 + -6
-47n = 50 + -6

Combine like terms: 50 + -6 = 44
-47n = 44

Divide each side by '-47'.
n = -0.9361702128

Simplifying
n = -0.9361702128