(2w-3)(3w+5)=0

Solution for (2w-3)(3w+5)=0 equation:

Simplifying
(2w + -3)(3w + 5) = 0

Reorder the terms:
(-3 + 2w)(3w + 5) = 0

Reorder the terms:
(-3 + 2w)(5 + 3w) = 0

Multiply (-3 + 2w) * (5 + 3w)
(-3(5 + 3w) + 2w * (5 + 3w)) = 0
((5 * -3 + 3w * -3) + 2w * (5 + 3w)) = 0
((-15 + -9w) + 2w * (5 + 3w)) = 0
(-15 + -9w + (5 * 2w + 3w * 2w)) = 0
(-15 + -9w + (10w + 6w2)) = 0

Combine like terms: -9w + 10w = 1w
(-15 + 1w + 6w2) = 0

Solving
-15 + 1w + 6w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-5 + -3w)(3 + -2w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

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

Combine like terms: 3 + -3 = 0
0 + -2w = 0 + -3
-2w = 0 + -3

Combine like terms: 0 + -3 = -3
-2w = -3

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {-1.666666667, 1.5}