(2w-1)w=190

Solution for (2w-1)w=190 equation:

Simplifying
(2w + -1) * w = 190

Reorder the terms:
(-1 + 2w) * w = 190

Reorder the terms for easier multiplication:
w(-1 + 2w) = 190
(-1 * w + 2w * w) = 190
(-1w + 2w2) = 190

Solving
-1w + 2w2 = 190

Solving for variable 'w'.

Reorder the terms:
-190 + -1w + 2w2 = 190 + -190

Combine like terms: 190 + -190 = 0
-190 + -1w + 2w2 = 0

Factor a trinomial.
(-19 + -2w)(10 + -1w) = 0

Subproblem 1
Set the factor '(-19 + -2w)' equal to zero and attempt to solve:

Simplifying
-19 + -2w = 0

Solving
-19 + -2w = 0

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

Add '19' to each side of the equation.
-19 + 19 + -2w = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2w = 0 + 19
-2w = 0 + 19

Combine like terms: 0 + 19 = 19
-2w = 19

Divide each side by '-2'.
w = -9.5

Simplifying
w = -9.5
Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve:

Simplifying
10 + -1w = 0

Solving
10 + -1w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1w = 0 + -10
-1w = 0 + -10

Combine like terms: 0 + -10 = -10
-1w = -10

Divide each side by '-1'.
w = 10

Simplifying
w = 10
Solution
w = {-9.5, 10}