(k+1)(8k-1)=45

Solution for (k+1)(8k-1)=45 equation:

Simplifying
(k + 1)(8k + -1) = 45

Reorder the terms:
(1 + k)(8k + -1) = 45

Reorder the terms:
(1 + k)(-1 + 8k) = 45

Multiply (1 + k) * (-1 + 8k)
(1(-1 + 8k) + k(-1 + 8k)) = 45
((-1 * 1 + 8k * 1) + k(-1 + 8k)) = 45
((-1 + 8k) + k(-1 + 8k)) = 45
(-1 + 8k + (-1 * k + 8k * k)) = 45
(-1 + 8k + (-1k + 8k2)) = 45

Combine like terms: 8k + -1k = 7k
(-1 + 7k + 8k2) = 45

Solving
-1 + 7k + 8k2 = 45

Solving for variable 'k'.

Reorder the terms:
-1 + -45 + 7k + 8k2 = 45 + -45

Combine like terms: -1 + -45 = -46
-46 + 7k + 8k2 = 45 + -45

Combine like terms: 45 + -45 = 0
-46 + 7k + 8k2 = 0

Factor a trinomial.
(-23 + -8k)(2 + -1k) = 0

Subproblem 1
Set the factor '(-23 + -8k)' equal to zero and attempt to solve:

Simplifying
-23 + -8k = 0

Solving
-23 + -8k = 0

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

Add '23' to each side of the equation.
-23 + 23 + -8k = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -8k = 0 + 23
-8k = 0 + 23

Combine like terms: 0 + 23 = 23
-8k = 23

Divide each side by '-8'.
k = -2.875

Simplifying
k = -2.875
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

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

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

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

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-2.875, 2}