k(2k+5)=12

Solution for k(2k+5)=12 equation:

Simplifying
k(2k + 5) = 12

Reorder the terms:
k(5 + 2k) = 12
(5 * k + 2k * k) = 12
(5k + 2k2) = 12

Solving
5k + 2k2 = 12

Solving for variable 'k'.

Reorder the terms:
-12 + 5k + 2k2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 5k + 2k2 = 0

Factor a trinomial.
(-4 + -1k)(3 + -2k) = 0

Subproblem 1
Set the factor '(-4 + -1k)' equal to zero and attempt to solve:

Simplifying
-4 + -1k = 0

Solving
-4 + -1k = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1k = 0 + 4
-1k = 0 + 4

Combine like terms: 0 + 4 = 4
-1k = 4

Divide each side by '-1'.
k = -4

Simplifying
k = -4
Subproblem 2
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
Solution
k = {-4, 1.5}