2(2n+3)=9n-3(n-3)

Solution for 2(2n+3)=9n-3(n-3) equation:

Simplifying
2(2n + 3) = 9n + -3(n + -3)

Reorder the terms:
2(3 + 2n) = 9n + -3(n + -3)
(3 * 2 + 2n * 2) = 9n + -3(n + -3)
(6 + 4n) = 9n + -3(n + -3)

Reorder the terms:
6 + 4n = 9n + -3(-3 + n)
6 + 4n = 9n + (-3 * -3 + n * -3)
6 + 4n = 9n + (9 + -3n)

Reorder the terms:
6 + 4n = 9 + 9n + -3n

Combine like terms: 9n + -3n = 6n
6 + 4n = 9 + 6n

Solving
6 + 4n = 9 + 6n

Solving for variable 'n'.

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

Add '-6n' to each side of the equation.
6 + 4n + -6n = 9 + 6n + -6n

Combine like terms: 4n + -6n = -2n
6 + -2n = 9 + 6n + -6n

Combine like terms: 6n + -6n = 0
6 + -2n = 9 + 0
6 + -2n = 9

Add '-6' to each side of the equation.
6 + -6 + -2n = 9 + -6

Combine like terms: 6 + -6 = 0
0 + -2n = 9 + -6
-2n = 9 + -6

Combine like terms: 9 + -6 = 3
-2n = 3

Divide each side by '-2'.
n = -1.5

Simplifying
n = -1.5