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

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

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

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

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

Solving
3 + 6k = -5 + 10k

Solving for variable 'k'.

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

Add '-10k' to each side of the equation.
3 + 6k + -10k = -5 + 10k + -10k

Combine like terms: 6k + -10k = -4k
3 + -4k = -5 + 10k + -10k

Combine like terms: 10k + -10k = 0
3 + -4k = -5 + 0
3 + -4k = -5

Add '-3' to each side of the equation.
3 + -3 + -4k = -5 + -3

Combine like terms: 3 + -3 = 0
0 + -4k = -5 + -3
-4k = -5 + -3

Combine like terms: -5 + -3 = -8
-4k = -8

Divide each side by '-4'.
k = 2

Simplifying
k = 2