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

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

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

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

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

Multiply (3 + 2k) * (-4 + k)
(3(-4 + k) + 2k * (-4 + k)) = 2(k + -3)
((-4 * 3 + k * 3) + 2k * (-4 + k)) = 2(k + -3)
((-12 + 3k) + 2k * (-4 + k)) = 2(k + -3)
(-12 + 3k + (-4 * 2k + k * 2k)) = 2(k + -3)
(-12 + 3k + (-8k + 2k2)) = 2(k + -3)

Combine like terms: 3k + -8k = -5k
(-12 + -5k + 2k2) = 2(k + -3)

Reorder the terms:
-12 + -5k + 2k2 = 2(-3 + k)
-12 + -5k + 2k2 = (-3 * 2 + k * 2)
-12 + -5k + 2k2 = (-6 + 2k)

Solving
-12 + -5k + 2k2 = -6 + 2k

Solving for variable 'k'.

Reorder the terms:
-12 + 6 + -5k + -2k + 2k2 = -6 + 2k + 6 + -2k

Combine like terms: -12 + 6 = -6
-6 + -5k + -2k + 2k2 = -6 + 2k + 6 + -2k

Combine like terms: -5k + -2k = -7k
-6 + -7k + 2k2 = -6 + 2k + 6 + -2k

Reorder the terms:
-6 + -7k + 2k2 = -6 + 6 + 2k + -2k

Combine like terms: -6 + 6 = 0
-6 + -7k + 2k2 = 0 + 2k + -2k
-6 + -7k + 2k2 = 2k + -2k

Combine like terms: 2k + -2k = 0
-6 + -7k + 2k2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-3 + -3.5k + k2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -3.5k + 3 + k2 = 0 + 3

Reorder the terms:
-3 + 3 + -3.5k + k2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -3.5k + k2 = 0 + 3
-3.5k + k2 = 0 + 3

Combine like terms: 0 + 3 = 3
-3.5k + k2 = 3

The k term is -3.5k.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5k + 3.0625 + k2 = 3 + 3.0625

Reorder the terms:
3.0625 + -3.5k + k2 = 3 + 3.0625

Combine like terms: 3 + 3.0625 = 6.0625
3.0625 + -3.5k + k2 = 6.0625

Factor a perfect square on the left side:
(k + -1.75)(k + -1.75) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(k + -1.75) equal to 2.46221445 and -2.46221445.

Subproblem 1
k + -1.75 = 2.46221445

Simplifying
k + -1.75 = 2.46221445

Reorder the terms:
-1.75 + k = 2.46221445

Solving
-1.75 + k = 2.46221445

Solving for variable 'k'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + k = 2.46221445 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + k = 2.46221445 + 1.75
k = 2.46221445 + 1.75

Combine like terms: 2.46221445 + 1.75 = 4.21221445
k = 4.21221445

Simplifying
k = 4.21221445

Subproblem 2
k + -1.75 = -2.46221445

Simplifying
k + -1.75 = -2.46221445

Reorder the terms:
-1.75 + k = -2.46221445

Solving
-1.75 + k = -2.46221445

Solving for variable 'k'.

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

Add '1.75' to each side of the equation.
-1.75 + 1.75 + k = -2.46221445 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + k = -2.46221445 + 1.75
k = -2.46221445 + 1.75

Combine like terms: -2.46221445 + 1.75 = -0.71221445
k = -0.71221445

Simplifying
k = -0.71221445

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {4.21221445, -0.71221445}