(w+3)(w+7)=

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

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

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

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

Multiply (3 + w) * (7 + w)
(3(7 + w) + w(7 + w)) = 0
((7 * 3 + w * 3) + w(7 + w)) = 0
((21 + 3w) + w(7 + w)) = 0
(21 + 3w + (7 * w + w * w)) = 0
(21 + 3w + (7w + w2)) = 0

Combine like terms: 3w + 7w = 10w
(21 + 10w + w2) = 0

Solving
21 + 10w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + w)(3 + w) = 0

Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve:

Simplifying
7 + w = 0

Solving
7 + w = 0

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

Add '-7' to each side of the equation.
7 + -7 + w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + w = 0 + -7
w = 0 + -7

Combine like terms: 0 + -7 = -7
w = -7

Simplifying
w = -7
Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 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 + w = 0 + -3

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

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

Simplifying
w = -3
Solution
w = {-7, -3}