(2w-1)(4w-3)=0

Solution for (2w-1)(4w-3)=0 equation:

Simplifying
(2w + -1)(4w + -3) = 0

Reorder the terms:
(-1 + 2w)(4w + -3) = 0

Reorder the terms:
(-1 + 2w)(-3 + 4w) = 0

Multiply (-1 + 2w) * (-3 + 4w)
(-1(-3 + 4w) + 2w * (-3 + 4w)) = 0
((-3 * -1 + 4w * -1) + 2w * (-3 + 4w)) = 0
((3 + -4w) + 2w * (-3 + 4w)) = 0
(3 + -4w + (-3 * 2w + 4w * 2w)) = 0
(3 + -4w + (-6w + 8w2)) = 0

Combine like terms: -4w + -6w = -10w
(3 + -10w + 8w2) = 0

Solving
3 + -10w + 8w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -2w)(3 + -4w) = 0

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

Simplifying
1 + -2w = 0

Solving
1 + -2w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2w = 0 + -1
-2w = 0 + -1

Combine like terms: 0 + -1 = -1
-2w = -1

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5
Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve:

Simplifying
3 + -4w = 0

Solving
3 + -4w = 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 + -4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4w = 0 + -3
-4w = 0 + -3

Combine like terms: 0 + -3 = -3
-4w = -3

Divide each side by '-4'.
w = 0.75

Simplifying
w = 0.75
Solution
w = {0.5, 0.75}