65=(2w-3)(w)

Solution for 65=(2w-3)(w) equation:

Simplifying
65 = (2w + -3)(w)

Reorder the terms:
65 = (-3 + 2w)(w)

Reorder the terms for easier multiplication:
65 = w(-3 + 2w)
65 = (-3 * w + 2w * w)
65 = (-3w + 2w2)

Solving
65 = -3w + 2w2

Solving for variable 'w'.

Reorder the terms:
65 + 3w + -2w2 = -3w + 3w + 2w2 + -2w2

Combine like terms: -3w + 3w = 0
65 + 3w + -2w2 = 0 + 2w2 + -2w2
65 + 3w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
65 + 3w + -2w2 = 0

Factor a trinomial.
(13 + -2w)(5 + w) = 0

Subproblem 1
Set the factor '(13 + -2w)' equal to zero and attempt to solve:

Simplifying
13 + -2w = 0

Solving
13 + -2w = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2w = 0 + -13
-2w = 0 + -13

Combine like terms: 0 + -13 = -13
-2w = -13

Divide each side by '-2'.
w = 6.5

Simplifying
w = 6.5
Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

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

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

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

Simplifying
w = -5
Solution
w = {6.5, -5}