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

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

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

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

Reorder the terms:
9 + 2n + -3n = 3 + -1(8n + 1)

Combine like terms: 2n + -3n = -1n
9 + -1n = 3 + -1(8n + 1)

Reorder the terms:
9 + -1n = 3 + -1(1 + 8n)
9 + -1n = 3 + (1 * -1 + 8n * -1)
9 + -1n = 3 + (-1 + -8n)

Combine like terms: 3 + -1 = 2
9 + -1n = 2 + -8n

Solving
9 + -1n = 2 + -8n

Solving for variable 'n'.

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

Add '8n' to each side of the equation.
9 + -1n + 8n = 2 + -8n + 8n

Combine like terms: -1n + 8n = 7n
9 + 7n = 2 + -8n + 8n

Combine like terms: -8n + 8n = 0
9 + 7n = 2 + 0
9 + 7n = 2

Add '-9' to each side of the equation.
9 + -9 + 7n = 2 + -9

Combine like terms: 9 + -9 = 0
0 + 7n = 2 + -9
7n = 2 + -9

Combine like terms: 2 + -9 = -7
7n = -7

Divide each side by '7'.
n = -1

Simplifying
n = -1