(3k-7)(k-4)=0

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Solution for (3k-7)(k-4)=0 equation: 


Simplifying
(3k + -7)(k + -4) = 0

Reorder the terms:
(-7 + 3k)(k + -4) = 0

Reorder the terms:
(-7 + 3k)(-4 + k) = 0

Multiply (-7 + 3k) * (-4 + k)
(-7(-4 + k) + 3k * (-4 + k)) = 0
((-4 * -7 + k * -7) + 3k * (-4 + k)) = 0
((28 + -7k) + 3k * (-4 + k)) = 0
(28 + -7k + (-4 * 3k + k * 3k)) = 0
(28 + -7k + (-12k + 3k2)) = 0

Combine like terms: -7k + -12k = -19k
(28 + -19k + 3k2) = 0

Solving
28 + -19k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(7 + -3k)(4 + -1k) = 0


Subproblem 1
Set the factor '(7 + -3k)' equal to zero and attempt to solve:

Simplifying
7 + -3k = 0

Solving
7 + -3k = 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 + -3k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3k = 0 + -7
-3k = 0 + -7

Combine like terms: 0 + -7 = -7
-3k = -7

Divide each side by '-3'.
k = 2.333333333

Simplifying
k = 2.333333333

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 = {2.333333333, 4}

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