3(k-2)-2(5k-1)=10

Solution for 3(k-2)-2(5k-1)=10 equation:

Simplifying
3(k + -2) + -2(5k + -1) = 10

Reorder the terms:
3(-2 + k) + -2(5k + -1) = 10
(-2 * 3 + k * 3) + -2(5k + -1) = 10
(-6 + 3k) + -2(5k + -1) = 10

Reorder the terms:
-6 + 3k + -2(-1 + 5k) = 10
-6 + 3k + (-1 * -2 + 5k * -2) = 10
-6 + 3k + (2 + -10k) = 10

Reorder the terms:
-6 + 2 + 3k + -10k = 10

Combine like terms: -6 + 2 = -4
-4 + 3k + -10k = 10

Combine like terms: 3k + -10k = -7k
-4 + -7k = 10

Solving
-4 + -7k = 10

Solving for variable 'k'.

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

Add '4' to each side of the equation.
-4 + 4 + -7k = 10 + 4

Combine like terms: -4 + 4 = 0
0 + -7k = 10 + 4
-7k = 10 + 4

Combine like terms: 10 + 4 = 14
-7k = 14

Divide each side by '-7'.
k = -2

Simplifying
k = -2