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

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


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

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

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

Multiply (-5 + 4k) * (-4 + k)
(-5(-4 + k) + 4k * (-4 + k)) = 0
((-4 * -5 + k * -5) + 4k * (-4 + k)) = 0
((20 + -5k) + 4k * (-4 + k)) = 0
(20 + -5k + (-4 * 4k + k * 4k)) = 0
(20 + -5k + (-16k + 4k2)) = 0

Combine like terms: -5k + -16k = -21k
(20 + -21k + 4k2) = 0

Solving
20 + -21k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + -4k)(4 + -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 '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {1.25, 4}

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