12=(2w+5)*w

Solution for 12=(2w+5)*w equation:

Simplifying
12 = (2w + 5) * w

Reorder the terms:
12 = (5 + 2w) * w

Reorder the terms for easier multiplication:
12 = w(5 + 2w)
12 = (5 * w + 2w * w)
12 = (5w + 2w2)

Solving
12 = 5w + 2w2

Solving for variable 'w'.

Reorder the terms:
12 + -5w + -2w2 = 5w + -5w + 2w2 + -2w2

Combine like terms: 5w + -5w = 0
12 + -5w + -2w2 = 0 + 2w2 + -2w2
12 + -5w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
12 + -5w + -2w2 = 0

Factor a trinomial.
(3 + -2w)(4 + w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

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

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

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

Simplifying
w = -4
Solution
w = {1.5, -4}