(2w+5)(w)=592

Solution for (2w+5)(w)=592 equation:

Simplifying
(2w + 5)(w) = 592

Reorder the terms:
(5 + 2w)(w) = 592

Reorder the terms for easier multiplication:
w(5 + 2w) = 592
(5 * w + 2w * w) = 592
(5w + 2w2) = 592

Solving
5w + 2w2 = 592

Solving for variable 'w'.

Reorder the terms:
-592 + 5w + 2w2 = 592 + -592

Combine like terms: 592 + -592 = 0
-592 + 5w + 2w2 = 0

Factor a trinomial.
(-37 + -2w)(16 + -1w) = 0

Subproblem 1
Set the factor '(-37 + -2w)' equal to zero and attempt to solve:

Simplifying
-37 + -2w = 0

Solving
-37 + -2w = 0

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

Add '37' to each side of the equation.
-37 + 37 + -2w = 0 + 37

Combine like terms: -37 + 37 = 0
0 + -2w = 0 + 37
-2w = 0 + 37

Combine like terms: 0 + 37 = 37
-2w = 37

Divide each side by '-2'.
w = -18.5

Simplifying
w = -18.5
Subproblem 2
Set the factor '(16 + -1w)' equal to zero and attempt to solve:

Simplifying
16 + -1w = 0

Solving
16 + -1w = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1w = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1w = 0 + -16
-1w = 0 + -16

Combine like terms: 0 + -16 = -16
-1w = -16

Divide each side by '-1'.
w = 16

Simplifying
w = 16
Solution
w = {-18.5, 16}