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

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

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

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

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

Multiply (1 + 3k) * (-2 + k)
(1(-2 + k) + 3k * (-2 + k)) = 0
((-2 * 1 + k * 1) + 3k * (-2 + k)) = 0
((-2 + 1k) + 3k * (-2 + k)) = 0
(-2 + 1k + (-2 * 3k + k * 3k)) = 0
(-2 + 1k + (-6k + 3k2)) = 0

Combine like terms: 1k + -6k = -5k
(-2 + -5k + 3k2) = 0

Solving
-2 + -5k + 3k2 = 0

Solving for variable 'k'.

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

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

Simplifying
-1 + -3k = 0

Solving
-1 + -3k = 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 + -3k = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3k = 0 + 1
-3k = 0 + 1

Combine like terms: 0 + 1 = 1
-3k = 1

Divide each side by '-3'.
k = -0.3333333333

Simplifying
k = -0.3333333333
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 = {-0.3333333333, 2}