5(2n+3)-(1-2n)=2(3(3+2n)-(3-n))

Solution for 5(2n+3)-(1-2n)=2(3(3+2n)-(3-n)) equation:

Simplifying
5(2n + 3) + -1(1 + -2n) = 2(3(3 + 2n) + -1(3 + -1n))

Reorder the terms:
5(3 + 2n) + -1(1 + -2n) = 2(3(3 + 2n) + -1(3 + -1n))
(3 * 5 + 2n * 5) + -1(1 + -2n) = 2(3(3 + 2n) + -1(3 + -1n))
(15 + 10n) + -1(1 + -2n) = 2(3(3 + 2n) + -1(3 + -1n))
15 + 10n + (1 * -1 + -2n * -1) = 2(3(3 + 2n) + -1(3 + -1n))
15 + 10n + (-1 + 2n) = 2(3(3 + 2n) + -1(3 + -1n))

Reorder the terms:
15 + -1 + 10n + 2n = 2(3(3 + 2n) + -1(3 + -1n))

Combine like terms: 15 + -1 = 14
14 + 10n + 2n = 2(3(3 + 2n) + -1(3 + -1n))

Combine like terms: 10n + 2n = 12n
14 + 12n = 2(3(3 + 2n) + -1(3 + -1n))
14 + 12n = 2((3 * 3 + 2n * 3) + -1(3 + -1n))
14 + 12n = 2((9 + 6n) + -1(3 + -1n))
14 + 12n = 2(9 + 6n + (3 * -1 + -1n * -1))
14 + 12n = 2(9 + 6n + (-3 + 1n))

Reorder the terms:
14 + 12n = 2(9 + -3 + 6n + 1n)

Combine like terms: 9 + -3 = 6
14 + 12n = 2(6 + 6n + 1n)

Combine like terms: 6n + 1n = 7n
14 + 12n = 2(6 + 7n)
14 + 12n = (6 * 2 + 7n * 2)
14 + 12n = (12 + 14n)

Solving
14 + 12n = 12 + 14n

Solving for variable 'n'.

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

Add '-14n' to each side of the equation.
14 + 12n + -14n = 12 + 14n + -14n

Combine like terms: 12n + -14n = -2n
14 + -2n = 12 + 14n + -14n

Combine like terms: 14n + -14n = 0
14 + -2n = 12 + 0
14 + -2n = 12

Add '-14' to each side of the equation.
14 + -14 + -2n = 12 + -14

Combine like terms: 14 + -14 = 0
0 + -2n = 12 + -14
-2n = 12 + -14

Combine like terms: 12 + -14 = -2
-2n = -2

Divide each side by '-2'.
n = 1

Simplifying
n = 1