(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 = 41w
(-42 + 41w + -5w2) = 0

Solving
-42 + 41w + -5w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(-7 + w)' equal to zero and attempt to solve:

Simplifying
-7 + w = 0

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

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

Combine like terms: 0 + 7 = 7
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}