(2w-7)(6-w)=0

Solution for (2w-7)(6-w)=0 equation:

Simplifying
(2w + -7)(6 + -1w) = 0

Reorder the terms:
(-7 + 2w)(6 + -1w) = 0

Multiply (-7 + 2w) * (6 + -1w)
(-7(6 + -1w) + 2w * (6 + -1w)) = 0
((6 * -7 + -1w * -7) + 2w * (6 + -1w)) = 0
((-42 + 7w) + 2w * (6 + -1w)) = 0
(-42 + 7w + (6 * 2w + -1w * 2w)) = 0
(-42 + 7w + (12w + -2w2)) = 0

Combine like terms: 7w + 12w = 19w
(-42 + 19w + -2w2) = 0

Solving
-42 + 19w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + w)(7 + -2w) = 0

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

Simplifying
-6 + w = 0

Solving
-6 + w = 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 + w = 0 + 6

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

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

Simplifying
w = 6
Subproblem 2
Set the factor '(7 + -2w)' equal to zero and attempt to solve:

Simplifying
7 + -2w = 0

Solving
7 + -2w = 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 + -2w = 0 + -7

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

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

Divide each side by '-2'.
w = 3.5

Simplifying
w = 3.5
Solution
w = {6, 3.5}