4(3n+1)-2=11(n-2)+21

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Solution for 4(3n+1)-2=11(n-2)+21 equation: 


Simplifying
4(3n + 1) + -2 = 11(n + -2) + 21

Reorder the terms:
4(1 + 3n) + -2 = 11(n + -2) + 21
(1 * 4 + 3n * 4) + -2 = 11(n + -2) + 21
(4 + 12n) + -2 = 11(n + -2) + 21

Reorder the terms:
4 + -2 + 12n = 11(n + -2) + 21

Combine like terms: 4 + -2 = 2
2 + 12n = 11(n + -2) + 21

Reorder the terms:
2 + 12n = 11(-2 + n) + 21
2 + 12n = (-2 * 11 + n * 11) + 21
2 + 12n = (-22 + 11n) + 21

Reorder the terms:
2 + 12n = -22 + 21 + 11n

Combine like terms: -22 + 21 = -1
2 + 12n = -1 + 11n

Solving
2 + 12n = -1 + 11n

Solving for variable 'n'.

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

Add '-11n' to each side of the equation.
2 + 12n + -11n = -1 + 11n + -11n

Combine like terms: 12n + -11n = 1n
2 + 1n = -1 + 11n + -11n

Combine like terms: 11n + -11n = 0
2 + 1n = -1 + 0
2 + 1n = -1

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

Combine like terms: 2 + -2 = 0
0 + 1n = -1 + -2
1n = -1 + -2

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

Divide each side by '1'.
n = -3

Simplifying
n = -3

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