(4k+7)(k+6)=0

Solution for (4k+7)(k+6)=0 equation:

Simplifying
(4k + 7)(k + 6) = 0

Reorder the terms:
(7 + 4k)(k + 6) = 0

Reorder the terms:
(7 + 4k)(6 + k) = 0

Multiply (7 + 4k) * (6 + k)
(7(6 + k) + 4k * (6 + k)) = 0
((6 * 7 + k * 7) + 4k * (6 + k)) = 0
((42 + 7k) + 4k * (6 + k)) = 0
(42 + 7k + (6 * 4k + k * 4k)) = 0
(42 + 7k + (24k + 4k2)) = 0

Combine like terms: 7k + 24k = 31k
(42 + 31k + 4k2) = 0

Solving
42 + 31k + 4k2 = 0

Solving for variable 'k'.

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

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

Simplifying
6 + k = 0

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

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

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

Simplifying
k = -6
Subproblem 2
Set the factor '(7 + 4k)' equal to zero and attempt to solve:

Simplifying
7 + 4k = 0

Solving
7 + 4k = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4k = 0 + -7
4k = 0 + -7

Combine like terms: 0 + -7 = -7
4k = -7

Divide each side by '4'.
k = -1.75

Simplifying
k = -1.75
Solution
k = {-6, -1.75}