3(4n-1)-(3n+2)=4(n-5)

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Solution for 3(4n-1)-(3n+2)=4(n-5) equation:


Simplifying
3(4n + -1) + -1(3n + 2) = 4(n + -5)

Reorder the terms:
3(-1 + 4n) + -1(3n + 2) = 4(n + -5)
(-1 * 3 + 4n * 3) + -1(3n + 2) = 4(n + -5)
(-3 + 12n) + -1(3n + 2) = 4(n + -5)

Reorder the terms:
-3 + 12n + -1(2 + 3n) = 4(n + -5)
-3 + 12n + (2 * -1 + 3n * -1) = 4(n + -5)
-3 + 12n + (-2 + -3n) = 4(n + -5)

Reorder the terms:
-3 + -2 + 12n + -3n = 4(n + -5)

Combine like terms: -3 + -2 = -5
-5 + 12n + -3n = 4(n + -5)

Combine like terms: 12n + -3n = 9n
-5 + 9n = 4(n + -5)

Reorder the terms:
-5 + 9n = 4(-5 + n)
-5 + 9n = (-5 * 4 + n * 4)
-5 + 9n = (-20 + 4n)

Solving
-5 + 9n = -20 + 4n

Solving for variable 'n'.

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

Add '-4n' to each side of the equation.
-5 + 9n + -4n = -20 + 4n + -4n

Combine like terms: 9n + -4n = 5n
-5 + 5n = -20 + 4n + -4n

Combine like terms: 4n + -4n = 0
-5 + 5n = -20 + 0
-5 + 5n = -20

Add '5' to each side of the equation.
-5 + 5 + 5n = -20 + 5

Combine like terms: -5 + 5 = 0
0 + 5n = -20 + 5
5n = -20 + 5

Combine like terms: -20 + 5 = -15
5n = -15

Divide each side by '5'.
n = -3

Simplifying
n = -3

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