5k^2+20k+100=160

Solution for 5k^2+20k+100=160 equation:

Simplifying
5k2 + 20k + 100 = 160

Reorder the terms:
100 + 20k + 5k2 = 160

Solving
100 + 20k + 5k2 = 160

Solving for variable 'k'.

Reorder the terms:
100 + -160 + 20k + 5k2 = 160 + -160

Combine like terms: 100 + -160 = -60
-60 + 20k + 5k2 = 160 + -160

Combine like terms: 160 + -160 = 0
-60 + 20k + 5k2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + 4k + k2) = 0

Factor a trinomial.
5((-6 + -1k)(2 + -1k)) = 0

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

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 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 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6
Subproblem 2
Set the factor '(2 + -1k)' equal to zero and attempt to solve:

Simplifying
2 + -1k = 0

Solving
2 + -1k = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1k = 0 + -2

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

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

Divide each side by '-1'.
k = 2

Simplifying
k = 2
Solution
k = {-6, 2}