9(k-2)=3k(k+4)

Solution for 9(k-2)=3k(k+4) equation:

Simplifying
9(k + -2) = 3k(k + 4)

Reorder the terms:
9(-2 + k) = 3k(k + 4)
(-2 * 9 + k * 9) = 3k(k + 4)
(-18 + 9k) = 3k(k + 4)

Reorder the terms:
-18 + 9k = 3k(4 + k)
-18 + 9k = (4 * 3k + k * 3k)
-18 + 9k = (12k + 3k2)

Solving
-18 + 9k = 12k + 3k2

Solving for variable 'k'.

Combine like terms: 9k + -12k = -3k
-18 + -3k + -3k2 = 12k + 3k2 + -12k + -3k2

Reorder the terms:
-18 + -3k + -3k2 = 12k + -12k + 3k2 + -3k2

Combine like terms: 12k + -12k = 0
-18 + -3k + -3k2 = 0 + 3k2 + -3k2
-18 + -3k + -3k2 = 3k2 + -3k2

Combine like terms: 3k2 + -3k2 = 0
-18 + -3k + -3k2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(6 + k + k2) = 0

Ignore the factor -3.
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.