(2k-5)(2k-5)=16

Solution for (2k-5)(2k-5)=16 equation:

Simplifying
(2k + -5)(2k + -5) = 16

Reorder the terms:
(-5 + 2k)(2k + -5) = 16

Reorder the terms:
(-5 + 2k)(-5 + 2k) = 16

Multiply (-5 + 2k) * (-5 + 2k)
(-5(-5 + 2k) + 2k * (-5 + 2k)) = 16
((-5 * -5 + 2k * -5) + 2k * (-5 + 2k)) = 16
((25 + -10k) + 2k * (-5 + 2k)) = 16
(25 + -10k + (-5 * 2k + 2k * 2k)) = 16
(25 + -10k + (-10k + 4k2)) = 16

Combine like terms: -10k + -10k = -20k
(25 + -20k + 4k2) = 16

Solving
25 + -20k + 4k2 = 16

Solving for variable 'k'.

Reorder the terms:
25 + -16 + -20k + 4k2 = 16 + -16

Combine like terms: 25 + -16 = 9
9 + -20k + 4k2 = 16 + -16

Combine like terms: 16 + -16 = 0
9 + -20k + 4k2 = 0

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

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

Simplifying
1 + -2k = 0

Solving
1 + -2k = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k = 0 + -1
-2k = 0 + -1

Combine like terms: 0 + -1 = -1
-2k = -1

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Subproblem 2
Set the factor '(9 + -2k)' equal to zero and attempt to solve:

Simplifying
9 + -2k = 0

Solving
9 + -2k = 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 + -2k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2k = 0 + -9
-2k = 0 + -9

Combine like terms: 0 + -9 = -9
-2k = -9

Divide each side by '-2'.
k = 4.5

Simplifying
k = 4.5
Solution
k = {0.5, 4.5}