(1+2w)w=45

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

Simplifying
(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}