10(4-k)+2=-2(k-3)-7

Solution for 10(4-k)+2=-2(k-3)-7 equation:

Simplifying
10(4 + -1k) + 2 = -2(k + -3) + -7
(4 * 10 + -1k * 10) + 2 = -2(k + -3) + -7
(40 + -10k) + 2 = -2(k + -3) + -7

Reorder the terms:
40 + 2 + -10k = -2(k + -3) + -7

Combine like terms: 40 + 2 = 42
42 + -10k = -2(k + -3) + -7

Reorder the terms:
42 + -10k = -2(-3 + k) + -7
42 + -10k = (-3 * -2 + k * -2) + -7
42 + -10k = (6 + -2k) + -7

Reorder the terms:
42 + -10k = 6 + -7 + -2k

Combine like terms: 6 + -7 = -1
42 + -10k = -1 + -2k

Solving
42 + -10k = -1 + -2k

Solving for variable 'k'.

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

Add '2k' to each side of the equation.
42 + -10k + 2k = -1 + -2k + 2k

Combine like terms: -10k + 2k = -8k
42 + -8k = -1 + -2k + 2k

Combine like terms: -2k + 2k = 0
42 + -8k = -1 + 0
42 + -8k = -1

Add '-42' to each side of the equation.
42 + -42 + -8k = -1 + -42

Combine like terms: 42 + -42 = 0
0 + -8k = -1 + -42
-8k = -1 + -42

Combine like terms: -1 + -42 = -43
-8k = -43

Divide each side by '-8'.
k = 5.375

Simplifying
k = 5.375