2[3(2k+1)-(k-3)]=5-3(2k-5)

Solution for 2[3(2k+1)-(k-3)]=5-3(2k-5) equation:

Simplifying
2[3(2k + 1) + -1(k + -3)] = 5 + -3(2k + -5)

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

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

Reorder the terms:
2[3 + 3 + 6k + -1k] = 5 + -3(2k + -5)

Combine like terms: 3 + 3 = 6
2[6 + 6k + -1k] = 5 + -3(2k + -5)

Combine like terms: 6k + -1k = 5k
2[6 + 5k] = 5 + -3(2k + -5)
[6 * 2 + 5k * 2] = 5 + -3(2k + -5)
[12 + 10k] = 5 + -3(2k + -5)

Reorder the terms:
12 + 10k = 5 + -3(-5 + 2k)
12 + 10k = 5 + (-5 * -3 + 2k * -3)
12 + 10k = 5 + (15 + -6k)

Combine like terms: 5 + 15 = 20
12 + 10k = 20 + -6k

Solving
12 + 10k = 20 + -6k

Solving for variable 'k'.

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

Add '6k' to each side of the equation.
12 + 10k + 6k = 20 + -6k + 6k

Combine like terms: 10k + 6k = 16k
12 + 16k = 20 + -6k + 6k

Combine like terms: -6k + 6k = 0
12 + 16k = 20 + 0
12 + 16k = 20

Add '-12' to each side of the equation.
12 + -12 + 16k = 20 + -12

Combine like terms: 12 + -12 = 0
0 + 16k = 20 + -12
16k = 20 + -12

Combine like terms: 20 + -12 = 8
16k = 8

Divide each side by '16'.
k = 0.5

Simplifying
k = 0.5