3+2k(k+1)=6+3k

Solution for 3+2k(k+1)=6+3k equation:

Simplifying
3 + 2k(k + 1) = 6 + 3k

Reorder the terms:
3 + 2k(1 + k) = 6 + 3k
3 + (1 * 2k + k * 2k) = 6 + 3k
3 + (2k + 2k2) = 6 + 3k

Solving
3 + 2k + 2k2 = 6 + 3k

Solving for variable 'k'.

Reorder the terms:
3 + -6 + 2k + -3k + 2k2 = 6 + 3k + -6 + -3k

Combine like terms: 3 + -6 = -3
-3 + 2k + -3k + 2k2 = 6 + 3k + -6 + -3k

Combine like terms: 2k + -3k = -1k
-3 + -1k + 2k2 = 6 + 3k + -6 + -3k

Reorder the terms:
-3 + -1k + 2k2 = 6 + -6 + 3k + -3k

Combine like terms: 6 + -6 = 0
-3 + -1k + 2k2 = 0 + 3k + -3k
-3 + -1k + 2k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
-3 + -1k + 2k2 = 0

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

Subproblem 1
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
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 = {-1, 1.5}