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

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

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

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

Multiply (3 + -1w) * (-6 + 4w)
(3(-6 + 4w) + -1w * (-6 + 4w)) = 0
((-6 * 3 + 4w * 3) + -1w * (-6 + 4w)) = 0
((-18 + 12w) + -1w * (-6 + 4w)) = 0
(-18 + 12w + (-6 * -1w + 4w * -1w)) = 0
(-18 + 12w + (6w + -4w2)) = 0

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

Solving
-18 + 18w + -4w2 = 0

Solving for variable 'w'.

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + w)' equal to zero and attempt to solve:

Simplifying
-3 + w = 0

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

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

Combine like terms: 0 + 3 = 3
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}