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

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


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

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

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

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

Combine like terms: 8 + 60 = 68
68 + -6k + 6k2 = (4k + 8) + -2(2k + 5)

Reorder the terms:
68 + -6k + 6k2 = (8 + 4k) + -2(2k + 5)

Remove parenthesis around (8 + 4k)
68 + -6k + 6k2 = 8 + 4k + -2(2k + 5)

Reorder the terms:
68 + -6k + 6k2 = 8 + 4k + -2(5 + 2k)
68 + -6k + 6k2 = 8 + 4k + (5 * -2 + 2k * -2)
68 + -6k + 6k2 = 8 + 4k + (-10 + -4k)

Reorder the terms:
68 + -6k + 6k2 = 8 + -10 + 4k + -4k

Combine like terms: 8 + -10 = -2
68 + -6k + 6k2 = -2 + 4k + -4k

Combine like terms: 4k + -4k = 0
68 + -6k + 6k2 = -2 + 0
68 + -6k + 6k2 = -2

Solving
68 + -6k + 6k2 = -2

Solving for variable 'k'.

Reorder the terms:
68 + 2 + -6k + 6k2 = -2 + 2

Combine like terms: 68 + 2 = 70
70 + -6k + 6k2 = -2 + 2

Combine like terms: -2 + 2 = 0
70 + -6k + 6k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(35 + -3k + 3k2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(35 + -3k + 3k2)' equal to zero and attempt to solve:

Simplifying
35 + -3k + 3k2 = 0

Solving
35 + -3k + 3k2 = 0

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

Divide each side by '3'.
11.66666667 + -1k + k2 = 0

Move the constant term to the right:

Add '-11.66666667' to each side of the equation.
11.66666667 + -1k + -11.66666667 + k2 = 0 + -11.66666667

Reorder the terms:
11.66666667 + -11.66666667 + -1k + k2 = 0 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + -1k + k2 = 0 + -11.66666667
-1k + k2 = 0 + -11.66666667

Combine like terms: 0 + -11.66666667 = -11.66666667
-1k + k2 = -11.66666667

The k term is -1k.  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.
-1k + 0.25 + k2 = -11.66666667 + 0.25

Reorder the terms:
0.25 + -1k + k2 = -11.66666667 + 0.25

Combine like terms: -11.66666667 + 0.25 = -11.41666667
0.25 + -1k + k2 = -11.41666667

Factor a perfect square on the left side:
(k + -0.5)(k + -0.5) = -11.41666667

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.

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