# 2(12-k)-(k+2)=8(2-3k)-3(5-6k)

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## Solution for 2(12-k)-(k+2)=8(2-3k)-3(5-6k) equation:

Simplifying
2(12 + -1k) + -1(k + 2) = 8(2 + -3k) + -3(5 + -6k)
(12 * 2 + -1k * 2) + -1(k + 2) = 8(2 + -3k) + -3(5 + -6k)
(24 + -2k) + -1(k + 2) = 8(2 + -3k) + -3(5 + -6k)

Reorder the terms:
24 + -2k + -1(2 + k) = 8(2 + -3k) + -3(5 + -6k)
24 + -2k + (2 * -1 + k * -1) = 8(2 + -3k) + -3(5 + -6k)
24 + -2k + (-2 + -1k) = 8(2 + -3k) + -3(5 + -6k)

Reorder the terms:
24 + -2 + -2k + -1k = 8(2 + -3k) + -3(5 + -6k)

Combine like terms: 24 + -2 = 22
22 + -2k + -1k = 8(2 + -3k) + -3(5 + -6k)

Combine like terms: -2k + -1k = -3k
22 + -3k = 8(2 + -3k) + -3(5 + -6k)
22 + -3k = (2 * 8 + -3k * 8) + -3(5 + -6k)
22 + -3k = (16 + -24k) + -3(5 + -6k)
22 + -3k = 16 + -24k + (5 * -3 + -6k * -3)
22 + -3k = 16 + -24k + (-15 + 18k)

Reorder the terms:
22 + -3k = 16 + -15 + -24k + 18k

Combine like terms: 16 + -15 = 1
22 + -3k = 1 + -24k + 18k

Combine like terms: -24k + 18k = -6k
22 + -3k = 1 + -6k

Solving
22 + -3k = 1 + -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.
22 + -3k + 6k = 1 + -6k + 6k

Combine like terms: -3k + 6k = 3k
22 + 3k = 1 + -6k + 6k

Combine like terms: -6k + 6k = 0
22 + 3k = 1 + 0
22 + 3k = 1

Add '-22' to each side of the equation.
22 + -22 + 3k = 1 + -22

Combine like terms: 22 + -22 = 0
0 + 3k = 1 + -22
3k = 1 + -22

Combine like terms: 1 + -22 = -21
3k = -21

Divide each side by '3'.
k = -7

Simplifying
k = -7`