(w)(2w+5)=250

Solution for (w)(2w+5)=250 equation:

Simplifying
(w)(2w + 5) = 250

Reorder the terms:
w(5 + 2w) = 250
(5 * w + 2w * w) = 250
(5w + 2w2) = 250

Solving
5w + 2w2 = 250

Solving for variable 'w'.

Reorder the terms:
-250 + 5w + 2w2 = 250 + -250

Combine like terms: 250 + -250 = 0
-250 + 5w + 2w2 = 0

Factor a trinomial.
(-25 + -2w)(10 + -1w) = 0

Subproblem 1
Set the factor '(-25 + -2w)' equal to zero and attempt to solve:

Simplifying
-25 + -2w = 0

Solving
-25 + -2w = 0

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

Add '25' to each side of the equation.
-25 + 25 + -2w = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2w = 0 + 25
-2w = 0 + 25

Combine like terms: 0 + 25 = 25
-2w = 25

Divide each side by '-2'.
w = -12.5

Simplifying
w = -12.5
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 = {-12.5, 10}