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

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

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

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

Multiply (-6 + 4w) * (3 + w)
(-6(3 + w) + 4w * (3 + w)) = 0
((3 * -6 + w * -6) + 4w * (3 + w)) = 0
((-18 + -6w) + 4w * (3 + w)) = 0
(-18 + -6w + (3 * 4w + w * 4w)) = 0
(-18 + -6w + (12w + 4w2)) = 0

Combine like terms: -6w + 12w = 6w
(-18 + 6w + 4w2) = 0

Solving
-18 + 6w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 3w + 2w2) = 0

Factor a trinomial.
2((-3 + -1w)(3 + -2w)) = 0

Ignore the factor 2.
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 '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 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 + -2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {-3, 1.5}