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

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

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

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

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