(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 = 5w
(42 + 5w + -2w2) = 0

Solving
42 + 5w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + -1w)(7 + 2w) = 0

Subproblem 1
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
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}