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

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

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

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

Multiply (3 + w) * (-5 + 3w)
(3(-5 + 3w) + w(-5 + 3w)) = 0
((-5 * 3 + 3w * 3) + w(-5 + 3w)) = 0
((-15 + 9w) + w(-5 + 3w)) = 0
(-15 + 9w + (-5 * w + 3w * w)) = 0
(-15 + 9w + (-5w + 3w2)) = 0

Combine like terms: 9w + -5w = 4w
(-15 + 4w + 3w2) = 0

Solving
-15 + 4w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(5 + -3w) = 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 '(5 + -3w)' equal to zero and attempt to solve:

Simplifying
5 + -3w = 0

Solving
5 + -3w = 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 + -3w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3w = 0 + -5
-3w = 0 + -5

Combine like terms: 0 + -5 = -5
-3w = -5

Divide each side by '-3'.
w = 1.666666667

Simplifying
w = 1.666666667
Solution
w = {-3, 1.666666667}