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

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

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

Reorder the terms:
3(-5 + 4n) + -4(5n + 1) = 5
(-5 * 3 + 4n * 3) + -4(5n + 1) = 5
(-15 + 12n) + -4(5n + 1) = 5

Reorder the terms:
-15 + 12n + -4(1 + 5n) = 5
-15 + 12n + (1 * -4 + 5n * -4) = 5
-15 + 12n + (-4 + -20n) = 5

Reorder the terms:
-15 + -4 + 12n + -20n = 5

Combine like terms: -15 + -4 = -19
-19 + 12n + -20n = 5

Combine like terms: 12n + -20n = -8n
-19 + -8n = 5

Solving
-19 + -8n = 5

Solving for variable 'n'.

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

Add '19' to each side of the equation.
-19 + 19 + -8n = 5 + 19

Combine like terms: -19 + 19 = 0
0 + -8n = 5 + 19
-8n = 5 + 19

Combine like terms: 5 + 19 = 24
-8n = 24

Divide each side by '-8'.
n = -3

Simplifying
n = -3