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

Solution for (2-w)(4w-6)=0 equation:

Simplifying
(2 + -1w)(4w + -6) = 0

Reorder the terms:
(2 + -1w)(-6 + 4w) = 0

Multiply (2 + -1w) * (-6 + 4w)
(2(-6 + 4w) + -1w * (-6 + 4w)) = 0
((-6 * 2 + 4w * 2) + -1w * (-6 + 4w)) = 0
((-12 + 8w) + -1w * (-6 + 4w)) = 0
(-12 + 8w + (-6 * -1w + 4w * -1w)) = 0
(-12 + 8w + (6w + -4w2)) = 0

Combine like terms: 8w + 6w = 14w
(-12 + 14w + -4w2) = 0

Solving
-12 + 14w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 7w + -2w2) = 0

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

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

Simplifying
-2 + w = 0

Solving
-2 + w = 0

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

Add '2' to each side of the equation.
-2 + 2 + w = 0 + 2

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

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

Simplifying
w = 2
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 = {2, 1.5}