(6-w)(3w+4)=0

Solution for (6-w)(3w+4)=0 equation:

Simplifying
(6 + -1w)(3w + 4) = 0

Reorder the terms:
(6 + -1w)(4 + 3w) = 0

Multiply (6 + -1w) * (4 + 3w)
(6(4 + 3w) + -1w * (4 + 3w)) = 0
((4 * 6 + 3w * 6) + -1w * (4 + 3w)) = 0
((24 + 18w) + -1w * (4 + 3w)) = 0
(24 + 18w + (4 * -1w + 3w * -1w)) = 0
(24 + 18w + (-4w + -3w2)) = 0

Combine like terms: 18w + -4w = 14w
(24 + 14w + -3w2) = 0

Solving
24 + 14w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + -1w)(4 + 3w) = 0

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

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

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

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

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

Simplifying
w = 6
Subproblem 2
Set the factor '(4 + 3w)' equal to zero and attempt to solve:

Simplifying
4 + 3w = 0

Solving
4 + 3w = 0

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

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

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

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

Divide each side by '3'.
w = -1.333333333

Simplifying
w = -1.333333333
Solution
w = {6, -1.333333333}