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

Solution for (1+w)(3w-5)=0 equation:

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

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

Multiply (1 + w) * (-5 + 3w)
(1(-5 + 3w) + w(-5 + 3w)) = 0
((-5 * 1 + 3w * 1) + w(-5 + 3w)) = 0
((-5 + 3w) + w(-5 + 3w)) = 0
(-5 + 3w + (-5 * w + 3w * w)) = 0
(-5 + 3w + (-5w + 3w2)) = 0

Combine like terms: 3w + -5w = -2w
(-5 + -2w + 3w2) = 0

Solving
-5 + -2w + 3w2 = 0

Solving for variable 'w'.

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

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 0

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

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

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

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

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

Simplifying
w = -1
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 = {-1, 1.666666667}