4k^2-20k=-9

Solution for 4k^2-20k=-9 equation:

Simplifying
4k2 + -20k = -9

Reorder the terms:
-20k + 4k2 = -9

Solving
-20k + 4k2 = -9

Solving for variable 'k'.

Reorder the terms:
9 + -20k + 4k2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -20k + 4k2 = 0

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

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

Simplifying
1 + -2k = 0

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

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

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

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Subproblem 2
Set the factor '(9 + -2k)' equal to zero and attempt to solve:

Simplifying
9 + -2k = 0

Solving
9 + -2k = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2k = 0 + -9
-2k = 0 + -9

Combine like terms: 0 + -9 = -9
-2k = -9

Divide each side by '-2'.
k = 4.5

Simplifying
k = 4.5
Solution
k = {0.5, 4.5}