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

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

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

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

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

Multiply (-4 + 3w) * (-6 + 4w)
(-4(-6 + 4w) + 3w * (-6 + 4w)) = 0
((-6 * -4 + 4w * -4) + 3w * (-6 + 4w)) = 0
((24 + -16w) + 3w * (-6 + 4w)) = 0
(24 + -16w + (-6 * 3w + 4w * 3w)) = 0
(24 + -16w + (-18w + 12w2)) = 0

Combine like terms: -16w + -18w = -34w
(24 + -34w + 12w2) = 0

Solving
24 + -34w + 12w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -17w + 6w2) = 0

Factor a trinomial.
2((4 + -3w)(3 + -2w)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {1.333333333, 1.5}