(3k-4)(6k-7)=0

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Solution for (3k-4)(6k-7)=0 equation: 


Simplifying
(3k + -4)(6k + -7) = 0

Reorder the terms:
(-4 + 3k)(6k + -7) = 0

Reorder the terms:
(-4 + 3k)(-7 + 6k) = 0

Multiply (-4 + 3k) * (-7 + 6k)
(-4(-7 + 6k) + 3k * (-7 + 6k)) = 0
((-7 * -4 + 6k * -4) + 3k * (-7 + 6k)) = 0
((28 + -24k) + 3k * (-7 + 6k)) = 0
(28 + -24k + (-7 * 3k + 6k * 3k)) = 0
(28 + -24k + (-21k + 18k2)) = 0

Combine like terms: -24k + -21k = -45k
(28 + -45k + 18k2) = 0

Solving
28 + -45k + 18k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(7 + -6k)(4 + -3k) = 0


Subproblem 1
Set the factor '(7 + -6k)' equal to zero and attempt to solve:

Simplifying
7 + -6k = 0

Solving
7 + -6k = 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 + -6k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6k = 0 + -7
-6k = 0 + -7

Combine like terms: 0 + -7 = -7
-6k = -7

Divide each side by '-6'.
k = 1.166666667

Simplifying
k = 1.166666667

Subproblem 2
Set the factor '(4 + -3k)' equal to zero and attempt to solve:

Simplifying
4 + -3k = 0

Solving
4 + -3k = 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 + -3k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3k = 0 + -4
-3k = 0 + -4

Combine like terms: 0 + -4 = -4
-3k = -4

Divide each side by '-3'.
k = 1.333333333

Simplifying
k = 1.333333333
Solution
k = {1.166666667, 1.333333333}

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