(4w-5)(6+w)=0

Solution for (4w-5)(6+w)=0 equation:

Simplifying
(4w + -5)(6 + w) = 0

Reorder the terms:
(-5 + 4w)(6 + w) = 0

Multiply (-5 + 4w) * (6 + w)
(-5(6 + w) + 4w * (6 + w)) = 0
((6 * -5 + w * -5) + 4w * (6 + w)) = 0
((-30 + -5w) + 4w * (6 + w)) = 0
(-30 + -5w + (6 * 4w + w * 4w)) = 0
(-30 + -5w + (24w + 4w2)) = 0

Combine like terms: -5w + 24w = 19w
(-30 + 19w + 4w2) = 0

Solving
-30 + 19w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + -1w)(5 + -4w) = 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 '(5 + -4w)' equal to zero and attempt to solve:

Simplifying
5 + -4w = 0

Solving
5 + -4w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -4w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4w = 0 + -5
-4w = 0 + -5

Combine like terms: 0 + -5 = -5
-4w = -5

Divide each side by '-4'.
w = 1.25

Simplifying
w = 1.25
Solution
w = {-6, 1.25}