3k*k-4=6-13k

Solution for 3k*k-4=6-13k equation:

Simplifying
3k * k + -4 = 6 + -13k

Multiply k * k
3k2 + -4 = 6 + -13k

Reorder the terms:
-4 + 3k2 = 6 + -13k

Solving
-4 + 3k2 = 6 + -13k

Solving for variable 'k'.

Reorder the terms:
-4 + -6 + 13k + 3k2 = 6 + -13k + -6 + 13k

Combine like terms: -4 + -6 = -10
-10 + 13k + 3k2 = 6 + -13k + -6 + 13k

Reorder the terms:
-10 + 13k + 3k2 = 6 + -6 + -13k + 13k

Combine like terms: 6 + -6 = 0
-10 + 13k + 3k2 = 0 + -13k + 13k
-10 + 13k + 3k2 = -13k + 13k

Combine like terms: -13k + 13k = 0
-10 + 13k + 3k2 = 0

Factor a trinomial.
(-5 + -1k)(2 + -3k) = 0

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

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 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 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -5
Subproblem 2
Set the factor '(2 + -3k)' equal to zero and attempt to solve:

Simplifying
2 + -3k = 0

Solving
2 + -3k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3k = 0 + -2

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

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

Divide each side by '-3'.
k = 0.6666666667

Simplifying
k = 0.6666666667
Solution
k = {-5, 0.6666666667}