(2W+1)(W)=45

Solution for (2W+1)(W)=45 equation:

Simplifying
(2W + 1)(W) = 45

Reorder the terms:
(1 + 2W)(W) = 45

Reorder the terms for easier multiplication:
W(1 + 2W) = 45
(1 * W + 2W * W) = 45
(1W + 2W2) = 45

Solving
1W + 2W2 = 45

Solving for variable 'W'.

Reorder the terms:
-45 + 1W + 2W2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 1W + 2W2 = 0

Factor a trinomial.
(-5 + -1W)(9 + -2W) = 0

Subproblem 1
Set the factor '(-5 + -1W)' equal to zero and attempt to solve:

Simplifying
-5 + -1W = 0

Solving
-5 + -1W = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1W = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1W = 0 + 5
-1W = 0 + 5

Combine like terms: 0 + 5 = 5
-1W = 5

Divide each side by '-1'.
W = -5

Simplifying
W = -5
Subproblem 2
Set the factor '(9 + -2W)' equal to zero and attempt to solve:

Simplifying
9 + -2W = 0

Solving
9 + -2W = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2W = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2W = 0 + -9
-2W = 0 + -9

Combine like terms: 0 + -9 = -9
-2W = -9

Divide each side by '-2'.
W = 4.5

Simplifying
W = 4.5
Solution
W = {-5, 4.5}