9(k-1)=-4k^2

Solution for 9(k-1)=-4k^2 equation:

Simplifying
9(k + -1) = -4k2

Reorder the terms:
9(-1 + k) = -4k2
(-1 * 9 + k * 9) = -4k2
(-9 + 9k) = -4k2

Solving
-9 + 9k = -4k2

Solving for variable 'k'.

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

Factor a trinomial.
(-3 + -1k)(3 + -4k) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -4k)' equal to zero and attempt to solve:

Simplifying
3 + -4k = 0

Solving
3 + -4k = 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 + -4k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4k = 0 + -3
-4k = 0 + -3

Combine like terms: 0 + -3 = -3
-4k = -3

Divide each side by '-4'.
k = 0.75

Simplifying
k = 0.75
Solution
k = {-3, 0.75}