(2k-7)(2k-3)=0

Solution for (2k-7)(2k-3)=0 equation:

Simplifying
(2k + -7)(2k + -3) = 0

Reorder the terms:
(-7 + 2k)(2k + -3) = 0

Reorder the terms:
(-7 + 2k)(-3 + 2k) = 0

Multiply (-7 + 2k) * (-3 + 2k)
(-7(-3 + 2k) + 2k * (-3 + 2k)) = 0
((-3 * -7 + 2k * -7) + 2k * (-3 + 2k)) = 0
((21 + -14k) + 2k * (-3 + 2k)) = 0
(21 + -14k + (-3 * 2k + 2k * 2k)) = 0
(21 + -14k + (-6k + 4k2)) = 0

Combine like terms: -14k + -6k = -20k
(21 + -20k + 4k2) = 0

Solving
21 + -20k + 4k2 = 0

Solving for variable 'k'.

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

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

Simplifying
3 + -2k = 0

Solving
3 + -2k = 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 + -2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2k = 0 + -3
-2k = 0 + -3

Combine like terms: 0 + -3 = -3
-2k = -3

Divide each side by '-2'.
k = 1.5

Simplifying
k = 1.5
Subproblem 2
Set the factor '(7 + -2k)' equal to zero and attempt to solve:

Simplifying
7 + -2k = 0

Solving
7 + -2k = 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 + -2k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2k = 0 + -7
-2k = 0 + -7

Combine like terms: 0 + -7 = -7
-2k = -7

Divide each side by '-2'.
k = 3.5

Simplifying
k = 3.5
Solution
k = {1.5, 3.5}