(5k+2)(k-1)=0

Solution for (5k+2)(k-1)=0 equation:

Simplifying
(5k + 2)(k + -1) = 0

Reorder the terms:
(2 + 5k)(k + -1) = 0

Reorder the terms:
(2 + 5k)(-1 + k) = 0

Multiply (2 + 5k) * (-1 + k)
(2(-1 + k) + 5k * (-1 + k)) = 0
((-1 * 2 + k * 2) + 5k * (-1 + k)) = 0
((-2 + 2k) + 5k * (-1 + k)) = 0
(-2 + 2k + (-1 * 5k + k * 5k)) = 0
(-2 + 2k + (-5k + 5k2)) = 0

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

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

Solving for variable 'k'.

Factor a trinomial.
(-2 + -5k)(1 + -1k) = 0

Subproblem 1
Set the factor '(-2 + -5k)' equal to zero and attempt to solve:

Simplifying
-2 + -5k = 0

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

Combine like terms: -2 + 2 = 0
0 + -5k = 0 + 2
-5k = 0 + 2

Combine like terms: 0 + 2 = 2
-5k = 2

Divide each side by '-5'.
k = -0.4

Simplifying
k = -0.4
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

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

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

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

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

Simplifying
k = 1
Solution
k = {-0.4, 1}