(3k+w)(k-6w)=

Solution for (3k+w)(k-6w)= equation:

Simplifying
(3k + w)(k + -6w) = 0

Multiply (3k + w) * (k + -6w)
(3k * (k + -6w) + w(k + -6w)) = 0
((k * 3k + -6w * 3k) + w(k + -6w)) = 0

Reorder the terms:
((-18kw + 3k2) + w(k + -6w)) = 0
((-18kw + 3k2) + w(k + -6w)) = 0
(-18kw + 3k2 + (k * w + -6w * w)) = 0
(-18kw + 3k2 + (kw + -6w2)) = 0

Reorder the terms:
(-18kw + kw + 3k2 + -6w2) = 0

Combine like terms: -18kw + kw = -17kw
(-17kw + 3k2 + -6w2) = 0

Solving
-17kw + 3k2 + -6w2 = 0

Solving for variable 'k'.

Factor a trinomial.
(k + -6w)(3k + w) = 0

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

Simplifying
k + -6w = 0

Solving
k + -6w = 0

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

Add '6w' to each side of the equation.
k + -6w + 6w = 0 + 6w

Combine like terms: -6w + 6w = 0
k + 0 = 0 + 6w
k = 0 + 6w
Remove the zero:
k = 6w

Simplifying
k = 6w
Subproblem 2
Set the factor '(3k + w)' equal to zero and attempt to solve:

Simplifying
3k + w = 0

Solving
3k + w = 0

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

Add '-1w' to each side of the equation.
3k + w + -1w = 0 + -1w

Combine like terms: w + -1w = 0
3k + 0 = 0 + -1w
3k = 0 + -1w
Remove the zero:
3k = -1w

Divide each side by '3'.
k = -0.3333333333w

Simplifying
k = -0.3333333333w
Solution
k = {6w, -0.3333333333w}