(x+3)(x+7)=

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

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

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

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

Multiply (3 + x) * (7 + x)
(3(7 + x) + x(7 + x)) = 0
((7 * 3 + x * 3) + x(7 + x)) = 0
((21 + 3x) + x(7 + x)) = 0
(21 + 3x + (7 * x + x * x)) = 0
(21 + 3x + (7x + x2)) = 0

Combine like terms: 3x + 7x = 10x
(21 + 10x + x2) = 0

Solving
21 + 10x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
7 + x = 0

Solving
7 + x = 0

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

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

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

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

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

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