12(2n+2)+3n=3(5n-12)+2n

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Solution for 12(2n+2)+3n=3(5n-12)+2n equation:


Simplifying
12(2n + 2) + 3n = 3(5n + -12) + 2n

Reorder the terms:
12(2 + 2n) + 3n = 3(5n + -12) + 2n
(2 * 12 + 2n * 12) + 3n = 3(5n + -12) + 2n
(24 + 24n) + 3n = 3(5n + -12) + 2n

Combine like terms: 24n + 3n = 27n
24 + 27n = 3(5n + -12) + 2n

Reorder the terms:
24 + 27n = 3(-12 + 5n) + 2n
24 + 27n = (-12 * 3 + 5n * 3) + 2n
24 + 27n = (-36 + 15n) + 2n

Combine like terms: 15n + 2n = 17n
24 + 27n = -36 + 17n

Solving
24 + 27n = -36 + 17n

Solving for variable 'n'.

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

Add '-17n' to each side of the equation.
24 + 27n + -17n = -36 + 17n + -17n

Combine like terms: 27n + -17n = 10n
24 + 10n = -36 + 17n + -17n

Combine like terms: 17n + -17n = 0
24 + 10n = -36 + 0
24 + 10n = -36

Add '-24' to each side of the equation.
24 + -24 + 10n = -36 + -24

Combine like terms: 24 + -24 = 0
0 + 10n = -36 + -24
10n = -36 + -24

Combine like terms: -36 + -24 = -60
10n = -60

Divide each side by '10'.
n = -6

Simplifying
n = -6

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