10k^2+3k-4=0

Solution for 10k^2+3k-4=0 equation:

Simplifying
10k2 + 3k + -4 = 0

Reorder the terms:
-4 + 3k + 10k2 = 0

Solving
-4 + 3k + 10k2 = 0

Solving for variable 'k'.

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

Subproblem 1
Set the factor '(-4 + -5k)' equal to zero and attempt to solve:

Simplifying
-4 + -5k = 0

Solving
-4 + -5k = 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 + -5k = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5k = 0 + 4
-5k = 0 + 4

Combine like terms: 0 + 4 = 4
-5k = 4

Divide each side by '-5'.
k = -0.8

Simplifying
k = -0.8
Subproblem 2
Set the factor '(1 + -2k)' equal to zero and attempt to solve:

Simplifying
1 + -2k = 0

Solving
1 + -2k = 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 + -2k = 0 + -1

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

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

Divide each side by '-2'.
k = 0.5

Simplifying
k = 0.5
Solution
k = {-0.8, 0.5}