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

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

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

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

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

Combine like terms: 24w + 5w = 29w
(30 + 29w + 4w2) = 0

Solving
30 + 29w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + w)(5 + 4w) = 0

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

Simplifying
6 + w = 0

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

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

Combine like terms: 0 + -6 = -6
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}