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

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


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

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

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

Multiply (-4 + k) * (-7 + 4k)
(-4(-7 + 4k) + k(-7 + 4k)) = 0
((-7 * -4 + 4k * -4) + k(-7 + 4k)) = 0
((28 + -16k) + k(-7 + 4k)) = 0
(28 + -16k + (-7 * k + 4k * k)) = 0
(28 + -16k + (-7k + 4k2)) = 0

Combine like terms: -16k + -7k = -23k
(28 + -23k + 4k2) = 0

Solving
28 + -23k + 4k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(7 + -4k)(4 + -1k) = 0


Subproblem 1
Set the factor '(7 + -4k)' equal to zero and attempt to solve:

Simplifying
7 + -4k = 0

Solving
7 + -4k = 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 + -4k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4k = 0 + -7
-4k = 0 + -7

Combine like terms: 0 + -7 = -7
-4k = -7

Divide each side by '-4'.
k = 1.75

Simplifying
k = 1.75

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 = {1.75, 4}

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