20k^2-90k+90=0

Solution for 20k^2-90k+90=0 equation:

Simplifying
20k2 + -90k + 90 = 0

Reorder the terms:
90 + -90k + 20k2 = 0

Solving
90 + -90k + 20k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '10'.
10(9 + -9k + 2k2) = 0

Factor a trinomial.
10((3 + -2k)(3 + -1k)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(3 + -2k)' equal to zero and attempt to solve:

Simplifying
3 + -2k = 0

Solving
3 + -2k = 0

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

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

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

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

Divide each side by '-2'.
k = 1.5

Simplifying
k = 1.5
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

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

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

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {1.5, 3}