2k^2+3k=20

Solution for 2k^2+3k=20 equation:

Simplifying
2k2 + 3k = 20

Reorder the terms:
3k + 2k2 = 20

Solving
3k + 2k2 = 20

Solving for variable 'k'.

Reorder the terms:
-20 + 3k + 2k2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 3k + 2k2 = 0

Factor a trinomial.
(-4 + -1k)(5 + -2k) = 0

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

Simplifying
5 + -2k = 0

Solving
5 + -2k = 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 + -2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2k = 0 + -5
-2k = 0 + -5

Combine like terms: 0 + -5 = -5
-2k = -5

Divide each side by '-2'.
k = 2.5

Simplifying
k = 2.5
Solution
k = {-4, 2.5}