5k^2-36k=-2k^2-5

Solution for 5k^2-36k=-2k^2-5 equation:

Simplifying
5k2 + -36k = -2k2 + -5

Reorder the terms:
-36k + 5k2 = -2k2 + -5

Reorder the terms:
-36k + 5k2 = -5 + -2k2

Solving
-36k + 5k2 = -5 + -2k2

Solving for variable 'k'.

Reorder the terms:
5 + -36k + 5k2 + 2k2 = -5 + -2k2 + 5 + 2k2

Combine like terms: 5k2 + 2k2 = 7k2
5 + -36k + 7k2 = -5 + -2k2 + 5 + 2k2

Reorder the terms:
5 + -36k + 7k2 = -5 + 5 + -2k2 + 2k2

Combine like terms: -5 + 5 = 0
5 + -36k + 7k2 = 0 + -2k2 + 2k2
5 + -36k + 7k2 = -2k2 + 2k2

Combine like terms: -2k2 + 2k2 = 0
5 + -36k + 7k2 = 0

Factor a trinomial.
(1 + -7k)(5 + -1k) = 0

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

Simplifying
1 + -7k = 0

Solving
1 + -7k = 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 + -7k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7k = 0 + -1
-7k = 0 + -1

Combine like terms: 0 + -1 = -1
-7k = -1

Divide each side by '-7'.
k = 0.1428571429

Simplifying
k = 0.1428571429
Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 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 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {0.1428571429, 5}