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

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

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

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

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

Multiply (1 + 3k) * (1 + k)
(1(1 + k) + 3k * (1 + k)) = 2k(k + 3)
((1 * 1 + k * 1) + 3k * (1 + k)) = 2k(k + 3)
((1 + 1k) + 3k * (1 + k)) = 2k(k + 3)
(1 + 1k + (1 * 3k + k * 3k)) = 2k(k + 3)
(1 + 1k + (3k + 3k2)) = 2k(k + 3)

Combine like terms: 1k + 3k = 4k
(1 + 4k + 3k2) = 2k(k + 3)

Reorder the terms:
1 + 4k + 3k2 = 2k(3 + k)
1 + 4k + 3k2 = (3 * 2k + k * 2k)
1 + 4k + 3k2 = (6k + 2k2)

Solving
1 + 4k + 3k2 = 6k + 2k2

Solving for variable 'k'.

Reorder the terms:
1 + 4k + -6k + 3k2 + -2k2 = 6k + 2k2 + -6k + -2k2

Combine like terms: 4k + -6k = -2k
1 + -2k + 3k2 + -2k2 = 6k + 2k2 + -6k + -2k2

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

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

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

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

Factor a trinomial.
(1 + -1k)(1 + -1k) = 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 '(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, 1}