w(2w+3)=5

Solution for w(2w+3)=5 equation:

Simplifying
w(2w + 3) = 5

Reorder the terms:
w(3 + 2w) = 5
(3 * w + 2w * w) = 5
(3w + 2w2) = 5

Solving
3w + 2w2 = 5

Solving for variable 'w'.

Reorder the terms:
-5 + 3w + 2w2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 3w + 2w2 = 0

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

Subproblem 1
Set the factor '(-5 + -2w)' equal to zero and attempt to solve:

Simplifying
-5 + -2w = 0

Solving
-5 + -2w = 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 + -2w = 0 + 5

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

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

Divide each side by '-2'.
w = -2.5

Simplifying
w = -2.5
Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve:

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Solution
w = {-2.5, 1}