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

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

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

Reorder the terms for easier multiplication:
3 * 3k * k + -4 = 6 + -13k

Multiply 3 * 3
9k * k + -4 = 6 + -13k

Multiply k * k
9k2 + -4 = 6 + -13k

Reorder the terms:
-4 + 9k2 = 6 + -13k

Solving
-4 + 9k2 = 6 + -13k

Solving for variable 'k'.

Reorder the terms:
-4 + -6 + 13k + 9k2 = 6 + -13k + -6 + 13k

Combine like terms: -4 + -6 = -10
-10 + 13k + 9k2 = 6 + -13k + -6 + 13k

Reorder the terms:
-10 + 13k + 9k2 = 6 + -6 + -13k + 13k

Combine like terms: 6 + -6 = 0
-10 + 13k + 9k2 = 0 + -13k + 13k
-10 + 13k + 9k2 = -13k + 13k

Combine like terms: -13k + 13k = 0
-10 + 13k + 9k2 = 0

Factor a trinomial.
(-2 + -1k)(5 + -9k) = 0

Subproblem 1
Set the factor '(-2 + -1k)' equal to zero and attempt to solve:

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 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 + -1k = 0 + 2

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

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

Divide each side by '-1'.
k = -2

Simplifying
k = -2
Subproblem 2
Set the factor '(5 + -9k)' equal to zero and attempt to solve:

Simplifying
5 + -9k = 0

Solving
5 + -9k = 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 + -9k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9k = 0 + -5
-9k = 0 + -5

Combine like terms: 0 + -5 = -5
-9k = -5

Divide each side by '-9'.
k = 0.5555555556

Simplifying
k = 0.5555555556
Solution
k = {-2, 0.5555555556}