k(2+3k)=5

Solution for k(2+3k)=5 equation:

Simplifying
k(2 + 3k) = 5
(2 * k + 3k * k) = 5
(2k + 3k2) = 5

Solving
2k + 3k2 = 5

Solving for variable 'k'.

Reorder the terms:
-5 + 2k + 3k2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 2k + 3k2 = 0

Factor a trinomial.
(-5 + -3k)(1 + -1k) = 0

Subproblem 1
Set the factor '(-5 + -3k)' equal to zero and attempt to solve:

Simplifying
-5 + -3k = 0

Solving
-5 + -3k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3k = 0 + 5
-3k = 0 + 5

Combine like terms: 0 + 5 = 5
-3k = 5

Divide each side by '-3'.
k = -1.666666667

Simplifying
k = -1.666666667
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 = {-1.666666667, 1}