12=(3w-5)w

Solution for 12=(3w-5)w equation:

Simplifying
12 = (3w + -5) * w

Reorder the terms:
12 = (-5 + 3w) * w

Reorder the terms for easier multiplication:
12 = w(-5 + 3w)
12 = (-5 * w + 3w * w)
12 = (-5w + 3w2)

Solving
12 = -5w + 3w2

Solving for variable 'w'.

Reorder the terms:
12 + 5w + -3w2 = -5w + 5w + 3w2 + -3w2

Combine like terms: -5w + 5w = 0
12 + 5w + -3w2 = 0 + 3w2 + -3w2
12 + 5w + -3w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
12 + 5w + -3w2 = 0

Factor a trinomial.
(3 + -1w)(4 + 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 '(4 + 3w)' equal to zero and attempt to solve:

Simplifying
4 + 3w = 0

Solving
4 + 3w = 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 + 3w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3w = 0 + -4
3w = 0 + -4

Combine like terms: 0 + -4 = -4
3w = -4

Divide each side by '3'.
w = -1.333333333

Simplifying
w = -1.333333333
Solution
w = {3, -1.333333333}