(4)(k^2+k-42)=0

Solution for (4)(k^2+k-42)=0 equation:

Simplifying
(4)(k2 + k + -42) = 0

Reorder the terms:
4(-42 + k + k2) = 0
(-42 * 4 + k * 4 + k2 * 4) = 0
(-168 + 4k + 4k2) = 0

Solving
-168 + 4k + 4k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-42 + k + k2) = 0

Factor a trinomial.
4((-7 + -1k)(6 + -1k)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-7 + -1k)' equal to zero and attempt to solve:

Simplifying
-7 + -1k = 0

Solving
-7 + -1k = 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 + -1k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1k = 0 + 7
-1k = 0 + 7

Combine like terms: 0 + 7 = 7
-1k = 7

Divide each side by '-1'.
k = -7

Simplifying
k = -7
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 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 + -1k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k = 0 + -6
-1k = 0 + -6

Combine like terms: 0 + -6 = -6
-1k = -6

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-7, 6}