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

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

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

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

Multiply (-4 + 3w) * (3 + w)
(-4(3 + w) + 3w * (3 + w)) = 0
((3 * -4 + w * -4) + 3w * (3 + w)) = 0
((-12 + -4w) + 3w * (3 + w)) = 0
(-12 + -4w + (3 * 3w + w * 3w)) = 0
(-12 + -4w + (9w + 3w2)) = 0

Combine like terms: -4w + 9w = 5w
(-12 + 5w + 3w2) = 0

Solving
-12 + 5w + 3w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 0

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

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

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3
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 = {-3, 1.333333333}