(w+6)(w+3)=10

Solution for (w+6)(w+3)=10 equation:

Simplifying
(w + 6)(w + 3) = 10

Reorder the terms:
(6 + w)(w + 3) = 10

Reorder the terms:
(6 + w)(3 + w) = 10

Multiply (6 + w) * (3 + w)
(6(3 + w) + w(3 + w)) = 10
((3 * 6 + w * 6) + w(3 + w)) = 10
((18 + 6w) + w(3 + w)) = 10
(18 + 6w + (3 * w + w * w)) = 10
(18 + 6w + (3w + w2)) = 10

Combine like terms: 6w + 3w = 9w
(18 + 9w + w2) = 10

Solving
18 + 9w + w2 = 10

Solving for variable 'w'.

Reorder the terms:
18 + -10 + 9w + w2 = 10 + -10

Combine like terms: 18 + -10 = 8
8 + 9w + w2 = 10 + -10

Combine like terms: 10 + -10 = 0
8 + 9w + w2 = 0

Factor a trinomial.
(8 + w)(1 + w) = 0

Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

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

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

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

Simplifying
w = -8
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

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

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

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

Simplifying
w = -1
Solution
w = {-8, -1}