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

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

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

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

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

Multiply (-5 + 2k) * (1 + 3k)
(-5(1 + 3k) + 2k * (1 + 3k)) = 3k(2k + -1)
((1 * -5 + 3k * -5) + 2k * (1 + 3k)) = 3k(2k + -1)
((-5 + -15k) + 2k * (1 + 3k)) = 3k(2k + -1)
(-5 + -15k + (1 * 2k + 3k * 2k)) = 3k(2k + -1)
(-5 + -15k + (2k + 6k2)) = 3k(2k + -1)

Combine like terms: -15k + 2k = -13k
(-5 + -13k + 6k2) = 3k(2k + -1)

Reorder the terms:
-5 + -13k + 6k2 = 3k(-1 + 2k)
-5 + -13k + 6k2 = (-1 * 3k + 2k * 3k)
-5 + -13k + 6k2 = (-3k + 6k2)

Add '-6k2' to each side of the equation.
-5 + -13k + 6k2 + -6k2 = -3k + 6k2 + -6k2

Combine like terms: 6k2 + -6k2 = 0
-5 + -13k + 0 = -3k + 6k2 + -6k2
-5 + -13k = -3k + 6k2 + -6k2

Combine like terms: 6k2 + -6k2 = 0
-5 + -13k = -3k + 0
-5 + -13k = -3k

Solving
-5 + -13k = -3k

Solving for variable 'k'.

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

Add '3k' to each side of the equation.
-5 + -13k + 3k = -3k + 3k

Combine like terms: -13k + 3k = -10k
-5 + -10k = -3k + 3k

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

Add '5' to each side of the equation.
-5 + 5 + -10k = 0 + 5

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

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

Divide each side by '-10'.
k = -0.5

Simplifying
k = -0.5