(2k-6)(7k-9)=

Solution for (2k-6)(7k-9)= equation:

Simplifying
(2k + -6)(7k + -9) = 0

Reorder the terms:
(-6 + 2k)(7k + -9) = 0

Reorder the terms:
(-6 + 2k)(-9 + 7k) = 0

Multiply (-6 + 2k) * (-9 + 7k)
(-6(-9 + 7k) + 2k * (-9 + 7k)) = 0
((-9 * -6 + 7k * -6) + 2k * (-9 + 7k)) = 0
((54 + -42k) + 2k * (-9 + 7k)) = 0
(54 + -42k + (-9 * 2k + 7k * 2k)) = 0
(54 + -42k + (-18k + 14k2)) = 0

Combine like terms: -42k + -18k = -60k
(54 + -60k + 14k2) = 0

Solving
54 + -60k + 14k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + -30k + 7k2) = 0

Factor a trinomial.
2((9 + -7k)(3 + -1k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + -7k)' equal to zero and attempt to solve:

Simplifying
9 + -7k = 0

Solving
9 + -7k = 0

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

Add '-9' to each side of the equation.
9 + -9 + -7k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7k = 0 + -9
-7k = 0 + -9

Combine like terms: 0 + -9 = -9
-7k = -9

Divide each side by '-7'.
k = 1.285714286

Simplifying
k = 1.285714286
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {1.285714286, 3}