14-3(5n-12)=1-(20n+1)

Solution for 14-3(5n-12)=1-(20n+1) equation:

Simplifying
14 + -3(5n + -12) = 1 + -1(20n + 1)

Reorder the terms:
14 + -3(-12 + 5n) = 1 + -1(20n + 1)
14 + (-12 * -3 + 5n * -3) = 1 + -1(20n + 1)
14 + (36 + -15n) = 1 + -1(20n + 1)

Combine like terms: 14 + 36 = 50
50 + -15n = 1 + -1(20n + 1)

Reorder the terms:
50 + -15n = 1 + -1(1 + 20n)
50 + -15n = 1 + (1 * -1 + 20n * -1)
50 + -15n = 1 + (-1 + -20n)

Combine like terms: 1 + -1 = 0
50 + -15n = 0 + -20n
50 + -15n = -20n

Solving
50 + -15n = -20n

Solving for variable 'n'.

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

Add '20n' to each side of the equation.
50 + -15n + 20n = -20n + 20n

Combine like terms: -15n + 20n = 5n
50 + 5n = -20n + 20n

Combine like terms: -20n + 20n = 0
50 + 5n = 0

Add '-50' to each side of the equation.
50 + -50 + 5n = 0 + -50

Combine like terms: 50 + -50 = 0
0 + 5n = 0 + -50
5n = 0 + -50

Combine like terms: 0 + -50 = -50
5n = -50

Divide each side by '5'.
n = -10

Simplifying
n = -10