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.
(4 + -3w)(3 + w) = 0

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

Simplifying
3 + w = 0

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

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

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

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