(k-7)(4k-5)=0

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Solution for (k-7)(4k-5)=0 equation: 


Simplifying
(k + -7)(4k + -5) = 0

Reorder the terms:
(-7 + k)(4k + -5) = 0

Reorder the terms:
(-7 + k)(-5 + 4k) = 0

Multiply (-7 + k) * (-5 + 4k)
(-7(-5 + 4k) + k(-5 + 4k)) = 0
((-5 * -7 + 4k * -7) + k(-5 + 4k)) = 0
((35 + -28k) + k(-5 + 4k)) = 0
(35 + -28k + (-5 * k + 4k * k)) = 0
(35 + -28k + (-5k + 4k2)) = 0

Combine like terms: -28k + -5k = -33k
(35 + -33k + 4k2) = 0

Solving
35 + -33k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(5 + -4k)(7 + -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 '(7 + -1k)' equal to zero and attempt to solve:

Simplifying
7 + -1k = 0

Solving
7 + -1k = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1k = 0 + -7
-1k = 0 + -7

Combine like terms: 0 + -7 = -7
-1k = -7

Divide each side by '-1'.
k = 7

Simplifying
k = 7
Solution
k = {1.25, 7}

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