(w+3)(w+4)+(w+2)(w+7)=

Solution for (w+3)(w+4)+(w+2)(w+7)= equation:

Simplifying
(w + 3)(w + 4) + (w + 2)(w + 7) = 0

Reorder the terms:
(3 + w)(w + 4) + (w + 2)(w + 7) = 0

Reorder the terms:
(3 + w)(4 + w) + (w + 2)(w + 7) = 0

Multiply (3 + w) * (4 + w)
(3(4 + w) + w(4 + w)) + (w + 2)(w + 7) = 0
((4 * 3 + w * 3) + w(4 + w)) + (w + 2)(w + 7) = 0
((12 + 3w) + w(4 + w)) + (w + 2)(w + 7) = 0
(12 + 3w + (4 * w + w * w)) + (w + 2)(w + 7) = 0
(12 + 3w + (4w + w2)) + (w + 2)(w + 7) = 0

Combine like terms: 3w + 4w = 7w
(12 + 7w + w2) + (w + 2)(w + 7) = 0

Reorder the terms:
12 + 7w + w2 + (2 + w)(w + 7) = 0

Reorder the terms:
12 + 7w + w2 + (2 + w)(7 + w) = 0

Multiply (2 + w) * (7 + w)
12 + 7w + w2 + (2(7 + w) + w(7 + w)) = 0
12 + 7w + w2 + ((7 * 2 + w * 2) + w(7 + w)) = 0
12 + 7w + w2 + ((14 + 2w) + w(7 + w)) = 0
12 + 7w + w2 + (14 + 2w + (7 * w + w * w)) = 0
12 + 7w + w2 + (14 + 2w + (7w + w2)) = 0

Combine like terms: 2w + 7w = 9w
12 + 7w + w2 + (14 + 9w + w2) = 0

Reorder the terms:
12 + 14 + 7w + 9w + w2 + w2 = 0

Combine like terms: 12 + 14 = 26
26 + 7w + 9w + w2 + w2 = 0

Combine like terms: 7w + 9w = 16w
26 + 16w + w2 + w2 = 0

Combine like terms: w2 + w2 = 2w2
26 + 16w + 2w2 = 0

Solving
26 + 16w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 8w + w2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13 + 8w + w2)' equal to zero and attempt to solve:

Simplifying
13 + 8w + w2 = 0

Solving
13 + 8w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 8w + -13 + w2 = 0 + -13

Reorder the terms:
13 + -13 + 8w + w2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 8w + w2 = 0 + -13
8w + w2 = 0 + -13

Combine like terms: 0 + -13 = -13
8w + w2 = -13

The w term is 8w.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8w + 16 + w2 = -13 + 16

Reorder the terms:
16 + 8w + w2 = -13 + 16

Combine like terms: -13 + 16 = 3
16 + 8w + w2 = 3

Factor a perfect square on the left side:
(w + 4)(w + 4) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(w + 4) equal to 1.732050808 and -1.732050808.

Subproblem 1
w + 4 = 1.732050808

Simplifying
w + 4 = 1.732050808

Reorder the terms:
4 + w = 1.732050808

Solving
4 + w = 1.732050808

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w = 1.732050808 + -4

Combine like terms: 4 + -4 = 0
0 + w = 1.732050808 + -4
w = 1.732050808 + -4

Combine like terms: 1.732050808 + -4 = -2.267949192
w = -2.267949192

Simplifying
w = -2.267949192

Subproblem 2
w + 4 = -1.732050808

Simplifying
w + 4 = -1.732050808

Reorder the terms:
4 + w = -1.732050808

Solving
4 + w = -1.732050808

Solving for variable 'w'.

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

Add '-4' to each side of the equation.
4 + -4 + w = -1.732050808 + -4

Combine like terms: 4 + -4 = 0
0 + w = -1.732050808 + -4
w = -1.732050808 + -4

Combine like terms: -1.732050808 + -4 = -5.732050808
w = -5.732050808

Simplifying
w = -5.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {-2.267949192, -5.732050808}
Solution
w = {-2.267949192, -5.732050808}