6(8k+7)(k-1)=0

Solution for 6(8k+7)(k-1)=0 equation:

Simplifying
6(8k + 7)(k + -1) = 0

Reorder the terms:
6(7 + 8k)(k + -1) = 0

Reorder the terms:
6(7 + 8k)(-1 + k) = 0

Multiply (7 + 8k) * (-1 + k)
6(7(-1 + k) + 8k * (-1 + k)) = 0
6((-1 * 7 + k * 7) + 8k * (-1 + k)) = 0
6((-7 + 7k) + 8k * (-1 + k)) = 0
6(-7 + 7k + (-1 * 8k + k * 8k)) = 0
6(-7 + 7k + (-8k + 8k2)) = 0

Combine like terms: 7k + -8k = -1k
6(-7 + -1k + 8k2) = 0
(-7 * 6 + -1k * 6 + 8k2 * 6) = 0
(-42 + -6k + 48k2) = 0

Solving
-42 + -6k + 48k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + -1k + 8k2) = 0

Factor a trinomial.
6((-7 + -8k)(1 + -1k)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + -8k)' equal to zero and attempt to solve:

Simplifying
-7 + -8k = 0

Solving
-7 + -8k = 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 + -8k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8k = 0 + 7
-8k = 0 + 7

Combine like terms: 0 + 7 = 7
-8k = 7

Divide each side by '-8'.
k = -0.875

Simplifying
k = -0.875
Subproblem 2
Set the factor '(1 + -1k)' equal to zero and attempt to solve:

Simplifying
1 + -1k = 0

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

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

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

Divide each side by '-1'.
k = 1

Simplifying
k = 1
Solution
k = {-0.875, 1}