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

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

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

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

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

Multiply (-6 + w) * (-4 + w)
(-6(-4 + w) + w(-4 + w)) = 0
((-4 * -6 + w * -6) + w(-4 + w)) = 0
((24 + -6w) + w(-4 + w)) = 0
(24 + -6w + (-4 * w + w * w)) = 0
(24 + -6w + (-4w + w2)) = 0

Combine like terms: -6w + -4w = -10w
(24 + -10w + w2) = 0

Solving
24 + -10w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(4 + -1w)(6 + -1w) = 0

Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 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 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {4, 6}