(2w-3)(w-2)=3

Solution for (2w-3)(w-2)=3 equation:

Simplifying
(2w + -3)(w + -2) = 3

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

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

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

Combine like terms: -3w + -4w = -7w
(6 + -7w + 2w2) = 3

Solving
6 + -7w + 2w2 = 3

Solving for variable 'w'.

Reorder the terms:
6 + -3 + -7w + 2w2 = 3 + -3

Combine like terms: 6 + -3 = 3
3 + -7w + 2w2 = 3 + -3

Combine like terms: 3 + -3 = 0
3 + -7w + 2w2 = 0

Factor a trinomial.
(1 + -2w)(3 + -1w) = 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 + -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
Solution
w = {0.5, 3}