(k+1)*(k+1)+4(k-2)+2k=0

Solution for (k+1)*(k+1)+4(k-2)+2k=0 equation:

Simplifying
(k + 1)(k + 1) + 4(k + -2) + 2k = 0

Reorder the terms:
(1 + k)(k + 1) + 4(k + -2) + 2k = 0

Reorder the terms:
(1 + k)(1 + k) + 4(k + -2) + 2k = 0

Multiply (1 + k) * (1 + k)
(1(1 + k) + k(1 + k)) + 4(k + -2) + 2k = 0
((1 * 1 + k * 1) + k(1 + k)) + 4(k + -2) + 2k = 0
((1 + 1k) + k(1 + k)) + 4(k + -2) + 2k = 0
(1 + 1k + (1 * k + k * k)) + 4(k + -2) + 2k = 0
(1 + 1k + (1k + k2)) + 4(k + -2) + 2k = 0

Combine like terms: 1k + 1k = 2k
(1 + 2k + k2) + 4(k + -2) + 2k = 0

Reorder the terms:
1 + 2k + k2 + 4(-2 + k) + 2k = 0
1 + 2k + k2 + (-2 * 4 + k * 4) + 2k = 0
1 + 2k + k2 + (-8 + 4k) + 2k = 0

Reorder the terms:
1 + -8 + 2k + 4k + 2k + k2 = 0

Combine like terms: 1 + -8 = -7
-7 + 2k + 4k + 2k + k2 = 0

Combine like terms: 2k + 4k = 6k
-7 + 6k + 2k + k2 = 0

Combine like terms: 6k + 2k = 8k
-7 + 8k + k2 = 0

Solving
-7 + 8k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 8k + 7 + k2 = 0 + 7

Reorder the terms:
-7 + 7 + 8k + k2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 8k + k2 = 0 + 7
8k + k2 = 0 + 7

Combine like terms: 0 + 7 = 7
8k + k2 = 7

The k term is 8k.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8k + 16 + k2 = 7 + 16

Reorder the terms:
16 + 8k + k2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + 8k + k2 = 23

Factor a perfect square on the left side:
(k + 4)(k + 4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(k + 4) equal to 4.795831523 and -4.795831523.

Subproblem 1
k + 4 = 4.795831523

Simplifying
k + 4 = 4.795831523

Reorder the terms:
4 + k = 4.795831523

Solving
4 + k = 4.795831523

Solving for variable 'k'.

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

Add '-4' to each side of the equation.
4 + -4 + k = 4.795831523 + -4

Combine like terms: 4 + -4 = 0
0 + k = 4.795831523 + -4
k = 4.795831523 + -4

Combine like terms: 4.795831523 + -4 = 0.795831523
k = 0.795831523

Simplifying
k = 0.795831523

Subproblem 2
k + 4 = -4.795831523

Simplifying
k + 4 = -4.795831523

Reorder the terms:
4 + k = -4.795831523

Solving
4 + k = -4.795831523

Solving for variable 'k'.

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

Add '-4' to each side of the equation.
4 + -4 + k = -4.795831523 + -4

Combine like terms: 4 + -4 = 0
0 + k = -4.795831523 + -4
k = -4.795831523 + -4

Combine like terms: -4.795831523 + -4 = -8.795831523
k = -8.795831523

Simplifying
k = -8.795831523

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {0.795831523, -8.795831523}