(k+3)-(5k-3)=(3k-11)(5k-3)

Solution for (k+3)-(5k-3)=(3k-11)(5k-3) equation:

Simplifying
(k + 3) + -1(5k + -3) = (3k + -11)(5k + -3)

Reorder the terms:
(3 + k) + -1(5k + -3) = (3k + -11)(5k + -3)

Remove parenthesis around (3 + k)
3 + k + -1(5k + -3) = (3k + -11)(5k + -3)

Reorder the terms:
3 + k + -1(-3 + 5k) = (3k + -11)(5k + -3)
3 + k + (-3 * -1 + 5k * -1) = (3k + -11)(5k + -3)
3 + k + (3 + -5k) = (3k + -11)(5k + -3)

Reorder the terms:
3 + 3 + k + -5k = (3k + -11)(5k + -3)

Combine like terms: 3 + 3 = 6
6 + k + -5k = (3k + -11)(5k + -3)

Combine like terms: k + -5k = -4k
6 + -4k = (3k + -11)(5k + -3)

Reorder the terms:
6 + -4k = (-11 + 3k)(5k + -3)

Reorder the terms:
6 + -4k = (-11 + 3k)(-3 + 5k)

Multiply (-11 + 3k) * (-3 + 5k)
6 + -4k = (-11(-3 + 5k) + 3k * (-3 + 5k))
6 + -4k = ((-3 * -11 + 5k * -11) + 3k * (-3 + 5k))
6 + -4k = ((33 + -55k) + 3k * (-3 + 5k))
6 + -4k = (33 + -55k + (-3 * 3k + 5k * 3k))
6 + -4k = (33 + -55k + (-9k + 15k2))

Combine like terms: -55k + -9k = -64k
6 + -4k = (33 + -64k + 15k2)

Solving
6 + -4k = 33 + -64k + 15k2

Solving for variable 'k'.

Reorder the terms:
6 + -33 + -4k + 64k + -15k2 = 33 + -64k + 15k2 + -33 + 64k + -15k2

Combine like terms: 6 + -33 = -27
-27 + -4k + 64k + -15k2 = 33 + -64k + 15k2 + -33 + 64k + -15k2

Combine like terms: -4k + 64k = 60k
-27 + 60k + -15k2 = 33 + -64k + 15k2 + -33 + 64k + -15k2

Reorder the terms:
-27 + 60k + -15k2 = 33 + -33 + -64k + 64k + 15k2 + -15k2

Combine like terms: 33 + -33 = 0
-27 + 60k + -15k2 = 0 + -64k + 64k + 15k2 + -15k2
-27 + 60k + -15k2 = -64k + 64k + 15k2 + -15k2

Combine like terms: -64k + 64k = 0
-27 + 60k + -15k2 = 0 + 15k2 + -15k2
-27 + 60k + -15k2 = 15k2 + -15k2

Combine like terms: 15k2 + -15k2 = 0
-27 + 60k + -15k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 20k + -5k2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-9 + 20k + -5k2)' equal to zero and attempt to solve:

Simplifying
-9 + 20k + -5k2 = 0

Solving
-9 + 20k + -5k2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
1.8 + -4k + k2 = 0

Move the constant term to the right:

Add '-1.8' to each side of the equation.
1.8 + -4k + -1.8 + k2 = 0 + -1.8

Reorder the terms:
1.8 + -1.8 + -4k + k2 = 0 + -1.8

Combine like terms: 1.8 + -1.8 = 0.0
0.0 + -4k + k2 = 0 + -1.8
-4k + k2 = 0 + -1.8

Combine like terms: 0 + -1.8 = -1.8
-4k + k2 = -1.8

The k term is -4k.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4k + 4 + k2 = -1.8 + 4

Reorder the terms:
4 + -4k + k2 = -1.8 + 4

Combine like terms: -1.8 + 4 = 2.2
4 + -4k + k2 = 2.2

Factor a perfect square on the left side:
(k + -2)(k + -2) = 2.2

Calculate the square root of the right side: 1.483239697

Break this problem into two subproblems by setting 
(k + -2) equal to 1.483239697 and -1.483239697.

Subproblem 1
k + -2 = 1.483239697

Simplifying
k + -2 = 1.483239697

Reorder the terms:
-2 + k = 1.483239697

Solving
-2 + k = 1.483239697

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = 1.483239697 + 2

Combine like terms: -2 + 2 = 0
0 + k = 1.483239697 + 2
k = 1.483239697 + 2

Combine like terms: 1.483239697 + 2 = 3.483239697
k = 3.483239697

Simplifying
k = 3.483239697

Subproblem 2
k + -2 = -1.483239697

Simplifying
k + -2 = -1.483239697

Reorder the terms:
-2 + k = -1.483239697

Solving
-2 + k = -1.483239697

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + 2 + k = -1.483239697 + 2

Combine like terms: -2 + 2 = 0
0 + k = -1.483239697 + 2
k = -1.483239697 + 2

Combine like terms: -1.483239697 + 2 = 0.516760303
k = 0.516760303

Simplifying
k = 0.516760303

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {3.483239697, 0.516760303}
Solution
k = {3.483239697, 0.516760303}