(4k+5)(k-1)=0

Solution for (4k+5)(k-1)=0 equation:

Simplifying
(4k + 5)(k + -1) = 0

Reorder the terms:
(5 + 4k)(k + -1) = 0

Reorder the terms:
(5 + 4k)(-1 + k) = 0

Multiply (5 + 4k) * (-1 + k)
(5(-1 + k) + 4k * (-1 + k)) = 0
((-1 * 5 + k * 5) + 4k * (-1 + k)) = 0
((-5 + 5k) + 4k * (-1 + k)) = 0
(-5 + 5k + (-1 * 4k + k * 4k)) = 0
(-5 + 5k + (-4k + 4k2)) = 0

Combine like terms: 5k + -4k = 1k
(-5 + 1k + 4k2) = 0

Solving
-5 + 1k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-5 + -4k)(1 + -1k) = 0

Subproblem 1
Set the factor '(-5 + -4k)' equal to zero and attempt to solve:

Simplifying
-5 + -4k = 0

Solving
-5 + -4k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4k = 0 + 5
-4k = 0 + 5

Combine like terms: 0 + 5 = 5
-4k = 5

Divide each side by '-4'.
k = -1.25

Simplifying
k = -1.25
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 = {-1.25, 1}