(4k-3)(7k+3)=0

Solution for (4k-3)(7k+3)=0 equation:

Simplifying
(4k + -3)(7k + 3) = 0

Reorder the terms:
(-3 + 4k)(7k + 3) = 0

Reorder the terms:
(-3 + 4k)(3 + 7k) = 0

Multiply (-3 + 4k) * (3 + 7k)
(-3(3 + 7k) + 4k * (3 + 7k)) = 0
((3 * -3 + 7k * -3) + 4k * (3 + 7k)) = 0
((-9 + -21k) + 4k * (3 + 7k)) = 0
(-9 + -21k + (3 * 4k + 7k * 4k)) = 0
(-9 + -21k + (12k + 28k2)) = 0

Combine like terms: -21k + 12k = -9k
(-9 + -9k + 28k2) = 0

Solving
-9 + -9k + 28k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-3 + -7k)(3 + -4k) = 0

Subproblem 1
Set the factor '(-3 + -7k)' equal to zero and attempt to solve:

Simplifying
-3 + -7k = 0

Solving
-3 + -7k = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7k = 0 + 3
-7k = 0 + 3

Combine like terms: 0 + 3 = 3
-7k = 3

Divide each side by '-7'.
k = -0.4285714286

Simplifying
k = -0.4285714286
Subproblem 2
Set the factor '(3 + -4k)' equal to zero and attempt to solve:

Simplifying
3 + -4k = 0

Solving
3 + -4k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4k = 0 + -3
-4k = 0 + -3

Combine like terms: 0 + -3 = -3
-4k = -3

Divide each side by '-4'.
k = 0.75

Simplifying
k = 0.75
Solution
k = {-0.4285714286, 0.75}