2k(-3k+4)+6(k+k+10)=k(4k+8)-2k(2k+5)

Solution for 2k(-3k+4)+6(k+k+10)=k(4k+8)-2k(2k+5) equation:

Simplifying
2k(-3k + 4) + 6(k + k + 10) = k(4k + 8) + -2k(2k + 5)

Reorder the terms:
2k(4 + -3k) + 6(k + k + 10) = k(4k + 8) + -2k(2k + 5)
(4 * 2k + -3k * 2k) + 6(k + k + 10) = k(4k + 8) + -2k(2k + 5)
(8k + -6k2) + 6(k + k + 10) = k(4k + 8) + -2k(2k + 5)

Reorder the terms:
8k + -6k2 + 6(10 + k + k) = k(4k + 8) + -2k(2k + 5)

Combine like terms: k + k = 2k
8k + -6k2 + 6(10 + 2k) = k(4k + 8) + -2k(2k + 5)
8k + -6k2 + (10 * 6 + 2k * 6) = k(4k + 8) + -2k(2k + 5)
8k + -6k2 + (60 + 12k) = k(4k + 8) + -2k(2k + 5)

Reorder the terms:
60 + 8k + 12k + -6k2 = k(4k + 8) + -2k(2k + 5)

Combine like terms: 8k + 12k = 20k
60 + 20k + -6k2 = k(4k + 8) + -2k(2k + 5)

Reorder the terms:
60 + 20k + -6k2 = k(8 + 4k) + -2k(2k + 5)
60 + 20k + -6k2 = (8 * k + 4k * k) + -2k(2k + 5)
60 + 20k + -6k2 = (8k + 4k2) + -2k(2k + 5)

Reorder the terms:
60 + 20k + -6k2 = 8k + 4k2 + -2k(5 + 2k)
60 + 20k + -6k2 = 8k + 4k2 + (5 * -2k + 2k * -2k)
60 + 20k + -6k2 = 8k + 4k2 + (-10k + -4k2)

Reorder the terms:
60 + 20k + -6k2 = 8k + -10k + 4k2 + -4k2

Combine like terms: 8k + -10k = -2k
60 + 20k + -6k2 = -2k + 4k2 + -4k2

Combine like terms: 4k2 + -4k2 = 0
60 + 20k + -6k2 = -2k + 0
60 + 20k + -6k2 = -2k

Solving
60 + 20k + -6k2 = -2k

Solving for variable 'k'.

Reorder the terms:
60 + 20k + 2k + -6k2 = -2k + 2k

Combine like terms: 20k + 2k = 22k
60 + 22k + -6k2 = -2k + 2k

Combine like terms: -2k + 2k = 0
60 + 22k + -6k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + 11k + -3k2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(30 + 11k + -3k2)' equal to zero and attempt to solve:

Simplifying
30 + 11k + -3k2 = 0

Solving
30 + 11k + -3k2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-10 + -3.666666667k + k2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -3.666666667k + 10 + k2 = 0 + 10

Reorder the terms:
-10 + 10 + -3.666666667k + k2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3.666666667k + k2 = 0 + 10
-3.666666667k + k2 = 0 + 10

Combine like terms: 0 + 10 = 10
-3.666666667k + k2 = 10

The k term is -3.666666667k.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667k + 3.361111114 + k2 = 10 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667k + k2 = 10 + 3.361111114

Combine like terms: 10 + 3.361111114 = 13.361111114
3.361111114 + -3.666666667k + k2 = 13.361111114

Factor a perfect square on the left side:
(k + -1.833333334)(k + -1.833333334) = 13.361111114

Calculate the square root of the right side: 3.655285367

Break this problem into two subproblems by setting 
(k + -1.833333334) equal to 3.655285367 and -3.655285367.

Subproblem 1
k + -1.833333334 = 3.655285367

Simplifying
k + -1.833333334 = 3.655285367

Reorder the terms:
-1.833333334 + k = 3.655285367

Solving
-1.833333334 + k = 3.655285367

Solving for variable 'k'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + k = 3.655285367 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + k = 3.655285367 + 1.833333334
k = 3.655285367 + 1.833333334

Combine like terms: 3.655285367 + 1.833333334 = 5.488618701
k = 5.488618701

Simplifying
k = 5.488618701

Subproblem 2
k + -1.833333334 = -3.655285367

Simplifying
k + -1.833333334 = -3.655285367

Reorder the terms:
-1.833333334 + k = -3.655285367

Solving
-1.833333334 + k = -3.655285367

Solving for variable 'k'.

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

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + k = -3.655285367 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + k = -3.655285367 + 1.833333334
k = -3.655285367 + 1.833333334

Combine like terms: -3.655285367 + 1.833333334 = -1.821952033
k = -1.821952033

Simplifying
k = -1.821952033

Solution
The solution to the problem is based on the solutions
from the subproblems.
k = {5.488618701, -1.821952033}
Solution
k = {5.488618701, -1.821952033}