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

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

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

Reorder the terms:
(-2 + 7n) + -1(-3n + 1) = -3(1 + -3n)

Remove parenthesis around (-2 + 7n)
-2 + 7n + -1(-3n + 1) = -3(1 + -3n)

Reorder the terms:
-2 + 7n + -1(1 + -3n) = -3(1 + -3n)
-2 + 7n + (1 * -1 + -3n * -1) = -3(1 + -3n)
-2 + 7n + (-1 + 3n) = -3(1 + -3n)

Reorder the terms:
-2 + -1 + 7n + 3n = -3(1 + -3n)

Combine like terms: -2 + -1 = -3
-3 + 7n + 3n = -3(1 + -3n)

Combine like terms: 7n + 3n = 10n
-3 + 10n = -3(1 + -3n)
-3 + 10n = (1 * -3 + -3n * -3)
-3 + 10n = (-3 + 9n)

Add '3' to each side of the equation.
-3 + 3 + 10n = -3 + 3 + 9n

Combine like terms: -3 + 3 = 0
0 + 10n = -3 + 3 + 9n
10n = -3 + 3 + 9n

Combine like terms: -3 + 3 = 0
10n = 0 + 9n
10n = 9n

Solving
10n = 9n

Solving for variable 'n'.

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

Add '-9n' to each side of the equation.
10n + -9n = 9n + -9n

Combine like terms: 10n + -9n = 1n
1n = 9n + -9n

Combine like terms: 9n + -9n = 0
1n = 0

Divide each side by '1'.
n = 0

Simplifying
n = 0