(2k-5)(k+2)=-9

Solution for (2k-5)(k+2)=-9 equation:

Simplifying
(2k + -5)(k + 2) = -9

Reorder the terms:
(-5 + 2k)(k + 2) = -9

Reorder the terms:
(-5 + 2k)(2 + k) = -9

Multiply (-5 + 2k) * (2 + k)
(-5(2 + k) + 2k * (2 + k)) = -9
((2 * -5 + k * -5) + 2k * (2 + k)) = -9
((-10 + -5k) + 2k * (2 + k)) = -9
(-10 + -5k + (2 * 2k + k * 2k)) = -9
(-10 + -5k + (4k + 2k2)) = -9

Combine like terms: -5k + 4k = -1k
(-10 + -1k + 2k2) = -9

Solving
-10 + -1k + 2k2 = -9

Solving for variable 'k'.

Reorder the terms:
-10 + 9 + -1k + 2k2 = -9 + 9

Combine like terms: -10 + 9 = -1
-1 + -1k + 2k2 = -9 + 9

Combine like terms: -9 + 9 = 0
-1 + -1k + 2k2 = 0

Factor a trinomial.
(-1 + -2k)(1 + -1k) = 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 '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

Solving
1 + -1k = 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 + -1k = 0 + -1

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

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

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

Simplifying
k = 1
Solution
k = {-0.5, 1}