21k^2-29k+13=3

Solution for 21k^2-29k+13=3 equation:

Simplifying
21k2 + -29k + 13 = 3

Reorder the terms:
13 + -29k + 21k2 = 3

Solving
13 + -29k + 21k2 = 3

Solving for variable 'k'.

Reorder the terms:
13 + -3 + -29k + 21k2 = 3 + -3

Combine like terms: 13 + -3 = 10
10 + -29k + 21k2 = 3 + -3

Combine like terms: 3 + -3 = 0
10 + -29k + 21k2 = 0

Factor a trinomial.
(2 + -3k)(5 + -7k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -7k)' equal to zero and attempt to solve:

Simplifying
5 + -7k = 0

Solving
5 + -7k = 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 + -7k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7k = 0 + -5
-7k = 0 + -5

Combine like terms: 0 + -5 = -5
-7k = -5

Divide each side by '-7'.
k = 0.7142857143

Simplifying
k = 0.7142857143
Solution
k = {0.6666666667, 0.7142857143}