3(1-6k^2)=25k

Solution for 3(1-6k^2)=25k equation:

Simplifying
3(1 + -6k2) = 25k
(1 * 3 + -6k2 * 3) = 25k
(3 + -18k2) = 25k

Solving
3 + -18k2 = 25k

Solving for variable 'k'.

Reorder the terms:
3 + -25k + -18k2 = 25k + -25k

Combine like terms: 25k + -25k = 0
3 + -25k + -18k2 = 0

Factor a trinomial.
(1 + -9k)(3 + 2k) = 0

Subproblem 1
Set the factor '(1 + -9k)' equal to zero and attempt to solve:

Simplifying
1 + -9k = 0

Solving
1 + -9k = 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 + -9k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -9k = 0 + -1
-9k = 0 + -1

Combine like terms: 0 + -1 = -1
-9k = -1

Divide each side by '-9'.
k = 0.1111111111

Simplifying
k = 0.1111111111
Subproblem 2
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
Solution
k = {0.1111111111, -1.5}