(4k-1)(3k+10)=0

Solution for (4k-1)(3k+10)=0 equation:

Simplifying
(4k + -1)(3k + 10) = 0

Reorder the terms:
(-1 + 4k)(3k + 10) = 0

Reorder the terms:
(-1 + 4k)(10 + 3k) = 0

Multiply (-1 + 4k) * (10 + 3k)
(-1(10 + 3k) + 4k * (10 + 3k)) = 0
((10 * -1 + 3k * -1) + 4k * (10 + 3k)) = 0
((-10 + -3k) + 4k * (10 + 3k)) = 0
(-10 + -3k + (10 * 4k + 3k * 4k)) = 0
(-10 + -3k + (40k + 12k2)) = 0

Combine like terms: -3k + 40k = 37k
(-10 + 37k + 12k2) = 0

Solving
-10 + 37k + 12k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-10 + -3k)(1 + -4k) = 0

Subproblem 1
Set the factor '(-10 + -3k)' equal to zero and attempt to solve:

Simplifying
-10 + -3k = 0

Solving
-10 + -3k = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3k = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3k = 0 + 10
-3k = 0 + 10

Combine like terms: 0 + 10 = 10
-3k = 10

Divide each side by '-3'.
k = -3.333333333

Simplifying
k = -3.333333333
Subproblem 2
Set the factor '(1 + -4k)' equal to zero and attempt to solve:

Simplifying
1 + -4k = 0

Solving
1 + -4k = 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 + -4k = 0 + -1

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

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

Divide each side by '-4'.
k = 0.25

Simplifying
k = 0.25
Solution
k = {-3.333333333, 0.25}