(w+5)(w+2)=40

Solution for (w+5)(w+2)=40 equation:

Simplifying
(w + 5)(w + 2) = 40

Reorder the terms:
(5 + w)(w + 2) = 40

Reorder the terms:
(5 + w)(2 + w) = 40

Multiply (5 + w) * (2 + w)
(5(2 + w) + w(2 + w)) = 40
((2 * 5 + w * 5) + w(2 + w)) = 40
((10 + 5w) + w(2 + w)) = 40
(10 + 5w + (2 * w + w * w)) = 40
(10 + 5w + (2w + w2)) = 40

Combine like terms: 5w + 2w = 7w
(10 + 7w + w2) = 40

Solving
10 + 7w + w2 = 40

Solving for variable 'w'.

Reorder the terms:
10 + -40 + 7w + w2 = 40 + -40

Combine like terms: 10 + -40 = -30
-30 + 7w + w2 = 40 + -40

Combine like terms: 40 + -40 = 0
-30 + 7w + w2 = 0

Factor a trinomial.
(-10 + -1w)(3 + -1w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-10, 3}