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

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

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

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

Multiply (-7 + 2w) * (6 + w)
(-7(6 + w) + 2w * (6 + w)) = 0
((6 * -7 + w * -7) + 2w * (6 + w)) = 0
((-42 + -7w) + 2w * (6 + w)) = 0
(-42 + -7w + (6 * 2w + w * 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}