(w-7)(w-3)=0

Solution for (w-7)(w-3)=0 equation:

Simplifying
(w + -7)(w + -3) = 0

Reorder the terms:
(-7 + w)(w + -3) = 0

Reorder the terms:
(-7 + w)(-3 + w) = 0

Multiply (-7 + w) * (-3 + w)
(-7(-3 + w) + w(-3 + w)) = 0
((-3 * -7 + w * -7) + w(-3 + w)) = 0
((21 + -7w) + w(-3 + w)) = 0
(21 + -7w + (-3 * w + w * w)) = 0
(21 + -7w + (-3w + w2)) = 0

Combine like terms: -7w + -3w = -10w
(21 + -10w + w2) = 0

Solving
21 + -10w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + -1w)(7 + -1w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve:

Simplifying
7 + -1w = 0

Solving
7 + -1w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1w = 0 + -7
-1w = 0 + -7

Combine like terms: 0 + -7 = -7
-1w = -7

Divide each side by '-1'.
w = 7

Simplifying
w = 7
Solution
w = {3, 7}