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

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


Simplifying
(7 + -1k)(k + -4) = 0

Reorder the terms:
(7 + -1k)(-4 + k) = 0

Multiply (7 + -1k) * (-4 + k)
(7(-4 + k) + -1k * (-4 + k)) = 0
((-4 * 7 + k * 7) + -1k * (-4 + k)) = 0
((-28 + 7k) + -1k * (-4 + k)) = 0
(-28 + 7k + (-4 * -1k + k * -1k)) = 0
(-28 + 7k + (4k + -1k2)) = 0

Combine like terms: 7k + 4k = 11k
(-28 + 11k + -1k2) = 0

Solving
-28 + 11k + -1k2 = 0

Solving for variable 'k'.

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


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

Simplifying
-7 + k = 0

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

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

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

Simplifying
k = 7

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 = {7, 4}

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