(w-7)(w-5)=0

Solution for (w-7)(w-5)=0 equation:

Simplifying
(w + -7)(w + -5) = 0

Reorder the terms:
(-7 + w)(w + -5) = 0

Reorder the terms:
(-7 + w)(-5 + w) = 0

Multiply (-7 + w) * (-5 + w)
(-7(-5 + w) + w(-5 + w)) = 0
((-5 * -7 + w * -7) + w(-5 + w)) = 0
((35 + -7w) + w(-5 + w)) = 0
(35 + -7w + (-5 * w + w * w)) = 0
(35 + -7w + (-5w + w2)) = 0

Combine like terms: -7w + -5w = -12w
(35 + -12w + w2) = 0

Solving
35 + -12w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + -1w)(7 + -1w) = 0

Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
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 = {5, 7}