(w+3.5)(2)+(w)(w)=31

Solution for (w+3.5)(2)+(w)(w)=31 equation:

Simplifying
(w + 3.5)(2) + (w)(w) = 31

Reorder the terms:
(3.5 + w)(2) + (w)(w) = 31

Reorder the terms for easier multiplication:
2(3.5 + w) + (w)(w) = 31
(3.5 * 2 + w * 2) + (w)(w) = 31
(7 + 2w) + (w)(w) = 31

Multiply w * w
7 + 2w + w2 = 31

Solving
7 + 2w + w2 = 31

Solving for variable 'w'.

Reorder the terms:
7 + -31 + 2w + w2 = 31 + -31

Combine like terms: 7 + -31 = -24
-24 + 2w + w2 = 31 + -31

Combine like terms: 31 + -31 = 0
-24 + 2w + w2 = 0

Factor a trinomial.
(-6 + -1w)(4 + -1w) = 0

Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve:

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1w = 0 + 6
-1w = 0 + 6

Combine like terms: 0 + 6 = 6
-1w = 6

Divide each side by '-1'.
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-6, 4}