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

Solution for (2k+1)(k-2)=0 equation:

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

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

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

Multiply (1 + 2k) * (-2 + k)
(1(-2 + k) + 2k * (-2 + k)) = 0
((-2 * 1 + k * 1) + 2k * (-2 + k)) = 0
((-2 + 1k) + 2k * (-2 + k)) = 0
(-2 + 1k + (-2 * 2k + k * 2k)) = 0
(-2 + 1k + (-4k + 2k2)) = 0

Combine like terms: 1k + -4k = -3k
(-2 + -3k + 2k2) = 0

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

Solving for variable 'k'.

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

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

Simplifying
-1 + -2k = 0

Solving
-1 + -2k = 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 + -2k = 0 + 1

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

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

Divide each side by '-2'.
k = -0.5

Simplifying
k = -0.5
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 = {-0.5, 2}