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

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

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

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

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

Combine like terms: -4w + 30w = 26w
(-24 + 26w + 5w2) = 0

Solving
-24 + 26w + 5w2 = 0

Solving for variable 'w'.

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

Simplifying
4 + -5w = 0

Solving
4 + -5w = 0

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

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

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

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

Divide each side by '-5'.
w = 0.8

Simplifying
w = 0.8
Solution
w = {-6, 0.8}