21=w(2w-1)

Solution for 21=w(2w-1) equation:

Simplifying
21 = w(2w + -1)

Reorder the terms:
21 = w(-1 + 2w)
21 = (-1 * w + 2w * w)
21 = (-1w + 2w2)

Solving
21 = -1w + 2w2

Solving for variable 'w'.

Reorder the terms:
21 + w + -2w2 = -1w + w + 2w2 + -2w2

Combine like terms: -1w + w = 0
21 + w + -2w2 = 0 + 2w2 + -2w2
21 + w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
21 + w + -2w2 = 0

Factor a trinomial.
(7 + -2w)(3 + w) = 0

Subproblem 1
Set the factor '(7 + -2w)' equal to zero and attempt to solve:

Simplifying
7 + -2w = 0

Solving
7 + -2w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2w = 0 + -7
-2w = 0 + -7

Combine like terms: 0 + -7 = -7
-2w = -7

Divide each side by '-2'.
w = 3.5

Simplifying
w = 3.5
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 = {3.5, -3}