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

Solution for (3+w)(5w-4)=0 equation:

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

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

Multiply (3 + w) * (-4 + 5w)
(3(-4 + 5w) + w(-4 + 5w)) = 0
((-4 * 3 + 5w * 3) + w(-4 + 5w)) = 0
((-12 + 15w) + w(-4 + 5w)) = 0
(-12 + 15w + (-4 * w + 5w * w)) = 0
(-12 + 15w + (-4w + 5w2)) = 0

Combine like terms: 15w + -4w = 11w
(-12 + 11w + 5w2) = 0

Solving
-12 + 11w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(4 + -5w) = 0

Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3
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 = {-3, 0.8}