(w-2)(w-5)=4

Solution for (w-2)(w-5)=4 equation:

Simplifying
(w + -2)(w + -5) = 4

Reorder the terms:
(-2 + w)(w + -5) = 4

Reorder the terms:
(-2 + w)(-5 + w) = 4

Multiply (-2 + w) * (-5 + w)
(-2(-5 + w) + w(-5 + w)) = 4
((-5 * -2 + w * -2) + w(-5 + w)) = 4
((10 + -2w) + w(-5 + w)) = 4
(10 + -2w + (-5 * w + w * w)) = 4
(10 + -2w + (-5w + w2)) = 4

Combine like terms: -2w + -5w = -7w
(10 + -7w + w2) = 4

Solving
10 + -7w + w2 = 4

Solving for variable 'w'.

Reorder the terms:
10 + -4 + -7w + w2 = 4 + -4

Combine like terms: 10 + -4 = 6
6 + -7w + w2 = 4 + -4

Combine like terms: 4 + -4 = 0
6 + -7w + w2 = 0

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

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

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
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 = {1, 6}