7(-2-k)=k(1+3k)

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Solution for 7(-2-k)=k(1+3k) equation: 


Simplifying
7(-2 + -1k) = k(1 + 3k)
(-2 * 7 + -1k * 7) = k(1 + 3k)
(-14 + -7k) = k(1 + 3k)
-14 + -7k = (1 * k + 3k * k)
-14 + -7k = (1k + 3k2)

Solving
-14 + -7k = 1k + 3k2

Solving for variable 'k'.

Combine like terms: -7k + -1k = -8k
-14 + -8k + -3k2 = 1k + 3k2 + -1k + -3k2

Reorder the terms:
-14 + -8k + -3k2 = 1k + -1k + 3k2 + -3k2

Combine like terms: 1k + -1k = 0
-14 + -8k + -3k2 = 0 + 3k2 + -3k2
-14 + -8k + -3k2 = 3k2 + -3k2

Combine like terms: 3k2 + -3k2 = 0
-14 + -8k + -3k2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 8k + 3k2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(14 + 8k + 3k2)' equal to zero and attempt to solve:

Simplifying
14 + 8k + 3k2 = 0

Solving
14 + 8k + 3k2 = 0

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

Divide each side by '3'.
4.666666667 + 2.666666667k + k2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + 2.666666667k + -4.666666667 + k2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + 2.666666667k + k2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + 2.666666667k + k2 = 0 + -4.666666667
2.666666667k + k2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
2.666666667k + k2 = -4.666666667

The k term is 2.666666667k.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667k + 1.777777780 + k2 = -4.666666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667k + k2 = -4.666666667 + 1.777777780

Combine like terms: -4.666666667 + 1.777777780 = -2.888888887
1.777777780 + 2.666666667k + k2 = -2.888888887

Factor a perfect square on the left side:
(k + 1.333333334)(k + 1.333333334) = -2.888888887

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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