(x+7)(x+3)=96

Solution for (x+7)(x+3)=96 equation:

Simplifying
(x + 7)(x + 3) = 96

Reorder the terms:
(7 + x)(x + 3) = 96

Reorder the terms:
(7 + x)(3 + x) = 96

Multiply (7 + x) * (3 + x)
(7(3 + x) + x(3 + x)) = 96
((3 * 7 + x * 7) + x(3 + x)) = 96
((21 + 7x) + x(3 + x)) = 96
(21 + 7x + (3 * x + x * x)) = 96
(21 + 7x + (3x + x2)) = 96

Combine like terms: 7x + 3x = 10x
(21 + 10x + x2) = 96

Solving
21 + 10x + x2 = 96

Solving for variable 'x'.

Reorder the terms:
21 + -96 + 10x + x2 = 96 + -96

Combine like terms: 21 + -96 = -75
-75 + 10x + x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-75 + 10x + x2 = 0

Factor a trinomial.
(-15 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve:

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-15, 5}