(2k+3)(k-9)=0

Solution for (2k+3)(k-9)=0 equation:

Simplifying
(2k + 3)(k + -9) = 0

Reorder the terms:
(3 + 2k)(k + -9) = 0

Reorder the terms:
(3 + 2k)(-9 + k) = 0

Multiply (3 + 2k) * (-9 + k)
(3(-9 + k) + 2k * (-9 + k)) = 0
((-9 * 3 + k * 3) + 2k * (-9 + k)) = 0
((-27 + 3k) + 2k * (-9 + k)) = 0
(-27 + 3k + (-9 * 2k + k * 2k)) = 0
(-27 + 3k + (-18k + 2k2)) = 0

Combine like terms: 3k + -18k = -15k
(-27 + -15k + 2k2) = 0

Solving
-27 + -15k + 2k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-3 + -2k)(9 + -1k) = 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 '(9 + -1k)' equal to zero and attempt to solve:

Simplifying
9 + -1k = 0

Solving
9 + -1k = 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 + -1k = 0 + -9

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

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

Divide each side by '-1'.
k = 9

Simplifying
k = 9
Solution
k = {-1.5, 9}