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

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

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

Combine like terms: -3 + 4 = 1
2k(1) + 6(k2 + 10) = k(4k + 8) + -2k(2k + 5)

Reorder the terms for easier multiplication:
2 * 1k + 6(k2 + 10) = k(4k + 8) + -2k(2k + 5)

Multiply 2 * 1
2k + 6(k2 + 10) = k(4k + 8) + -2k(2k + 5)

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

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

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

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

Reorder the terms:
60 + 2k + 6k2 = 8k + -10k + 4k2 + -4k2

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

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

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

Solving for variable 'k'.

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

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

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

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

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

Simplifying
30 + 2k + 3k2 = 0

Solving
30 + 2k + 3k2 = 0

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

Divide each side by '3'.
10 + 0.6666666667k + k2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 0.6666666667k + -10 + k2 = 0 + -10

Reorder the terms:
10 + -10 + 0.6666666667k + k2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 0.6666666667k + k2 = 0 + -10
0.6666666667k + k2 = 0 + -10

Combine like terms: 0 + -10 = -10
0.6666666667k + k2 = -10

The k term is 0.6666666667k.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667k + 0.1111111112 + k2 = -10 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667k + k2 = -10 + 0.1111111112

Combine like terms: -10 + 0.1111111112 = -9.8888888888
0.1111111112 + 0.6666666667k + k2 = -9.8888888888

Factor a perfect square on the left side:
(k + 0.3333333334)(k + 0.3333333334) = -9.8888888888

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.