(2w-5)(w)=33

Solution for (2w-5)(w)=33 equation:

Simplifying
(2w + -5)(w) = 33

Reorder the terms:
(-5 + 2w)(w) = 33

Reorder the terms for easier multiplication:
w(-5 + 2w) = 33
(-5 * w + 2w * w) = 33
(-5w + 2w2) = 33

Solving
-5w + 2w2 = 33

Solving for variable 'w'.

Reorder the terms:
-33 + -5w + 2w2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + -5w + 2w2 = 0

Factor a trinomial.
(-3 + -1w)(11 + -2w) = 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 '(11 + -2w)' equal to zero and attempt to solve:

Simplifying
11 + -2w = 0

Solving
11 + -2w = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2w = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2w = 0 + -11
-2w = 0 + -11

Combine like terms: 0 + -11 = -11
-2w = -11

Divide each side by '-2'.
w = 5.5

Simplifying
w = 5.5
Solution
w = {-3, 5.5}