(k+1)*(3k-1)=

Solution for (k+1)*(3k-1)= equation:

Simplifying
(k + 1)(3k + -1) = 0

Reorder the terms:
(1 + k)(3k + -1) = 0

Reorder the terms:
(1 + k)(-1 + 3k) = 0

Multiply (1 + k) * (-1 + 3k)
(1(-1 + 3k) + k(-1 + 3k)) = 0
((-1 * 1 + 3k * 1) + k(-1 + 3k)) = 0
((-1 + 3k) + k(-1 + 3k)) = 0
(-1 + 3k + (-1 * k + 3k * k)) = 0
(-1 + 3k + (-1k + 3k2)) = 0

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

Solving
-1 + 2k + 3k2 = 0

Solving for variable 'k'.

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

Simplifying
1 + -3k = 0

Solving
1 + -3k = 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 + -3k = 0 + -1

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

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

Divide each side by '-3'.
k = 0.3333333333

Simplifying
k = 0.3333333333
Solution
k = {-1, 0.3333333333}