25k^2-132k=-120-2k

Solution for 25k^2-132k=-120-2k equation:

Simplifying
25k2 + -132k = -120 + -2k

Reorder the terms:
-132k + 25k2 = -120 + -2k

Solving
-132k + 25k2 = -120 + -2k

Solving for variable 'k'.

Reorder the terms:
120 + -132k + 2k + 25k2 = -120 + -2k + 120 + 2k

Combine like terms: -132k + 2k = -130k
120 + -130k + 25k2 = -120 + -2k + 120 + 2k

Reorder the terms:
120 + -130k + 25k2 = -120 + 120 + -2k + 2k

Combine like terms: -120 + 120 = 0
120 + -130k + 25k2 = 0 + -2k + 2k
120 + -130k + 25k2 = -2k + 2k

Combine like terms: -2k + 2k = 0
120 + -130k + 25k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + -26k + 5k2) = 0

Factor a trinomial.
5((6 + -5k)(4 + -1k)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(6 + -5k)' equal to zero and attempt to solve:

Simplifying
6 + -5k = 0

Solving
6 + -5k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5k = 0 + -6
-5k = 0 + -6

Combine like terms: 0 + -6 = -6
-5k = -6

Divide each side by '-5'.
k = 1.2

Simplifying
k = 1.2
Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {1.2, 4}