(7-w)(5w+6)=0

Solution for (7-w)(5w+6)=0 equation:

Simplifying
(7 + -1w)(5w + 6) = 0

Reorder the terms:
(7 + -1w)(6 + 5w) = 0

Multiply (7 + -1w) * (6 + 5w)
(7(6 + 5w) + -1w * (6 + 5w)) = 0
((6 * 7 + 5w * 7) + -1w * (6 + 5w)) = 0
((42 + 35w) + -1w * (6 + 5w)) = 0
(42 + 35w + (6 * -1w + 5w * -1w)) = 0
(42 + 35w + (-6w + -5w2)) = 0

Combine like terms: 35w + -6w = 29w
(42 + 29w + -5w2) = 0

Solving
42 + 29w + -5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + -1w)(6 + 5w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + 5w)' equal to zero and attempt to solve:

Simplifying
6 + 5w = 0

Solving
6 + 5w = 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 + 5w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5w = 0 + -6
5w = 0 + -6

Combine like terms: 0 + -6 = -6
5w = -6

Divide each side by '5'.
w = -1.2

Simplifying
w = -1.2
Solution
w = {7, -1.2}