2k(-3k+4)+6(k^2+10)=k(4k+8)-2k(7k+5)

Solution for 2k(-3k+4)+6(k^2+10)=k(4k+8)-2k(7k+5) equation:

Simplifying
2k(-3k + 4) + 6(k2 + 10) = k(4k + 8) + -2k(7k + 5)

Reorder the terms:
2k(4 + -3k) + 6(k2 + 10) = k(4k + 8) + -2k(7k + 5)
(4 * 2k + -3k * 2k) + 6(k2 + 10) = k(4k + 8) + -2k(7k + 5)
(8k + -6k2) + 6(k2 + 10) = k(4k + 8) + -2k(7k + 5)

Reorder the terms:
8k + -6k2 + 6(10 + k2) = k(4k + 8) + -2k(7k + 5)
8k + -6k2 + (10 * 6 + k2 * 6) = k(4k + 8) + -2k(7k + 5)
8k + -6k2 + (60 + 6k2) = k(4k + 8) + -2k(7k + 5)

Reorder the terms:
60 + 8k + -6k2 + 6k2 = k(4k + 8) + -2k(7k + 5)

Combine like terms: -6k2 + 6k2 = 0
60 + 8k + 0 = k(4k + 8) + -2k(7k + 5)
60 + 8k = k(4k + 8) + -2k(7k + 5)

Reorder the terms:
60 + 8k = k(8 + 4k) + -2k(7k + 5)
60 + 8k = (8 * k + 4k * k) + -2k(7k + 5)
60 + 8k = (8k + 4k2) + -2k(7k + 5)

Reorder the terms:
60 + 8k = 8k + 4k2 + -2k(5 + 7k)
60 + 8k = 8k + 4k2 + (5 * -2k + 7k * -2k)
60 + 8k = 8k + 4k2 + (-10k + -14k2)

Reorder the terms:
60 + 8k = 8k + -10k + 4k2 + -14k2

Combine like terms: 8k + -10k = -2k
60 + 8k = -2k + 4k2 + -14k2

Combine like terms: 4k2 + -14k2 = -10k2
60 + 8k = -2k + -10k2

Solving
60 + 8k = -2k + -10k2

Solving for variable 'k'.

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

Reorder the terms:
60 + 10k + 10k2 = -2k + 2k + -10k2 + 10k2

Combine like terms: -2k + 2k = 0
60 + 10k + 10k2 = 0 + -10k2 + 10k2
60 + 10k + 10k2 = -10k2 + 10k2

Combine like terms: -10k2 + 10k2 = 0
60 + 10k + 10k2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(6 + k + k2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(6 + k + k2)' equal to zero and attempt to solve:

Simplifying
6 + k + k2 = 0

Solving
6 + k + k2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + k + -6 + k2 = 0 + -6

Reorder the terms:
6 + -6 + k + k2 = 0 + -6

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

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

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
k + 0.25 + k2 = -6 + 0.25

Reorder the terms:
0.25 + k + k2 = -6 + 0.25

Combine like terms: -6 + 0.25 = -5.75
0.25 + k + k2 = -5.75

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = -5.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.