4(4k+1)-8(k-1)=3(2k+1)-1

Solution for 4(4k+1)-8(k-1)=3(2k+1)-1 equation:

Simplifying
4(4k + 1) + -8(k + -1) = 3(2k + 1) + -1

Reorder the terms:
4(1 + 4k) + -8(k + -1) = 3(2k + 1) + -1
(1 * 4 + 4k * 4) + -8(k + -1) = 3(2k + 1) + -1
(4 + 16k) + -8(k + -1) = 3(2k + 1) + -1

Reorder the terms:
4 + 16k + -8(-1 + k) = 3(2k + 1) + -1
4 + 16k + (-1 * -8 + k * -8) = 3(2k + 1) + -1
4 + 16k + (8 + -8k) = 3(2k + 1) + -1

Reorder the terms:
4 + 8 + 16k + -8k = 3(2k + 1) + -1

Combine like terms: 4 + 8 = 12
12 + 16k + -8k = 3(2k + 1) + -1

Combine like terms: 16k + -8k = 8k
12 + 8k = 3(2k + 1) + -1

Reorder the terms:
12 + 8k = 3(1 + 2k) + -1
12 + 8k = (1 * 3 + 2k * 3) + -1
12 + 8k = (3 + 6k) + -1

Reorder the terms:
12 + 8k = 3 + -1 + 6k

Combine like terms: 3 + -1 = 2
12 + 8k = 2 + 6k

Solving
12 + 8k = 2 + 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 + 8k + -6k = 2 + 6k + -6k

Combine like terms: 8k + -6k = 2k
12 + 2k = 2 + 6k + -6k

Combine like terms: 6k + -6k = 0
12 + 2k = 2 + 0
12 + 2k = 2

Add '-12' to each side of the equation.
12 + -12 + 2k = 2 + -12

Combine like terms: 12 + -12 = 0
0 + 2k = 2 + -12
2k = 2 + -12

Combine like terms: 2 + -12 = -10
2k = -10

Divide each side by '2'.
k = -5

Simplifying
k = -5