3(k+1)11k=2(4+5k)+3

Solution for 3(k+1)11k=2(4+5k)+3 equation:

Simplifying
3(k + 1) * 11k = 2(4 + 5k) + 3

Reorder the terms:
3(1 + k) * 11k = 2(4 + 5k) + 3

Reorder the terms for easier multiplication:
3 * 11k(1 + k) = 2(4 + 5k) + 3

Multiply 3 * 11
33k(1 + k) = 2(4 + 5k) + 3
(1 * 33k + k * 33k) = 2(4 + 5k) + 3
(33k + 33k2) = 2(4 + 5k) + 3
33k + 33k2 = (4 * 2 + 5k * 2) + 3
33k + 33k2 = (8 + 10k) + 3

Reorder the terms:
33k + 33k2 = 8 + 3 + 10k

Combine like terms: 8 + 3 = 11
33k + 33k2 = 11 + 10k

Solving
33k + 33k2 = 11 + 10k

Solving for variable 'k'.

Reorder the terms:
-11 + 33k + -10k + 33k2 = 11 + 10k + -11 + -10k

Combine like terms: 33k + -10k = 23k
-11 + 23k + 33k2 = 11 + 10k + -11 + -10k

Reorder the terms:
-11 + 23k + 33k2 = 11 + -11 + 10k + -10k

Combine like terms: 11 + -11 = 0
-11 + 23k + 33k2 = 0 + 10k + -10k
-11 + 23k + 33k2 = 10k + -10k

Combine like terms: 10k + -10k = 0
-11 + 23k + 33k2 = 0

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

Divide each side by '33'.
-0.3333333333 + 0.696969697k + k2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.696969697k + 0.3333333333 + k2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.696969697k + k2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.696969697k + k2 = 0 + 0.3333333333
0.696969697k + k2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.696969697k + k2 = 0.3333333333

The k term is 0.696969697k.  Take half its coefficient (0.3484848485).
Square it (0.1214416896) and add it to both sides.

Add '0.1214416896' to each side of the equation.
0.696969697k + 0.1214416896 + k2 = 0.3333333333 + 0.1214416896

Reorder the terms:
0.1214416896 + 0.696969697k + k2 = 0.3333333333 + 0.1214416896

Combine like terms: 0.3333333333 + 0.1214416896 = 0.4547750229
0.1214416896 + 0.696969697k + k2 = 0.4547750229

Factor a perfect square on the left side:
(k + 0.3484848485)(k + 0.3484848485) = 0.4547750229

Calculate the square root of the right side: 0.674370093

Break this problem into two subproblems by setting 
(k + 0.3484848485) equal to 0.674370093 and -0.674370093.

Subproblem 1
k + 0.3484848485 = 0.674370093

Simplifying
k + 0.3484848485 = 0.674370093

Reorder the terms:
0.3484848485 + k = 0.674370093

Solving
0.3484848485 + k = 0.674370093

Solving for variable 'k'.

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

Add '-0.3484848485' to each side of the equation.
0.3484848485 + -0.3484848485 + k = 0.674370093 + -0.3484848485

Combine like terms: 0.3484848485 + -0.3484848485 = 0.0000000000
0.0000000000 + k = 0.674370093 + -0.3484848485
k = 0.674370093 + -0.3484848485

Combine like terms: 0.674370093 + -0.3484848485 = 0.3258852445
k = 0.3258852445

Simplifying
k = 0.3258852445

Subproblem 2
k + 0.3484848485 = -0.674370093

Simplifying
k + 0.3484848485 = -0.674370093

Reorder the terms:
0.3484848485 + k = -0.674370093

Solving
0.3484848485 + k = -0.674370093

Solving for variable 'k'.

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

Add '-0.3484848485' to each side of the equation.
0.3484848485 + -0.3484848485 + k = -0.674370093 + -0.3484848485

Combine like terms: 0.3484848485 + -0.3484848485 = 0.0000000000
0.0000000000 + k = -0.674370093 + -0.3484848485
k = -0.674370093 + -0.3484848485

Combine like terms: -0.674370093 + -0.3484848485 = -1.0228549415
k = -1.0228549415

Simplifying
k = -1.0228549415

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.3258852445, -1.0228549415}