(3k-6)(2k+4k+1)=

Solution for (3k-6)(2k+4k+1)= equation:

Simplifying
(3k + -6)(2k + 4k + 1) = 0

Reorder the terms:
(-6 + 3k)(2k + 4k + 1) = 0

Reorder the terms:
(-6 + 3k)(1 + 2k + 4k) = 0

Combine like terms: 2k + 4k = 6k
(-6 + 3k)(1 + 6k) = 0

Multiply (-6 + 3k) * (1 + 6k)
(-6(1 + 6k) + 3k * (1 + 6k)) = 0
((1 * -6 + 6k * -6) + 3k * (1 + 6k)) = 0
((-6 + -36k) + 3k * (1 + 6k)) = 0
(-6 + -36k + (1 * 3k + 6k * 3k)) = 0
(-6 + -36k + (3k + 18k2)) = 0

Combine like terms: -36k + 3k = -33k
(-6 + -33k + 18k2) = 0

Solving
-6 + -33k + 18k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + -11k + 6k2) = 0

Factor a trinomial.
3((-1 + -6k)(2 + -1k)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + -6k)' equal to zero and attempt to solve:

Simplifying
-1 + -6k = 0

Solving
-1 + -6k = 0

Move all terms containing k to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -6k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6k = 0 + 1
-6k = 0 + 1

Combine like terms: 0 + 1 = 1
-6k = 1

Divide each side by '-6'.
k = -0.1666666667

Simplifying
k = -0.1666666667
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1k = 0 + -2
-1k = 0 + -2

Combine like terms: 0 + -2 = -2
-1k = -2

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-0.1666666667, 2}