(x+7)*(x+5)=3

Solution for (x+7)*(x+5)=3 equation:

Simplifying
(x + 7)(x + 5) = 3

Reorder the terms:
(7 + x)(x + 5) = 3

Reorder the terms:
(7 + x)(5 + x) = 3

Multiply (7 + x) * (5 + x)
(7(5 + x) + x(5 + x)) = 3
((5 * 7 + x * 7) + x(5 + x)) = 3
((35 + 7x) + x(5 + x)) = 3
(35 + 7x + (5 * x + x * x)) = 3
(35 + 7x + (5x + x2)) = 3

Combine like terms: 7x + 5x = 12x
(35 + 12x + x2) = 3

Solving
35 + 12x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
35 + -3 + 12x + x2 = 3 + -3

Combine like terms: 35 + -3 = 32
32 + 12x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
32 + 12x + x2 = 0

Factor a trinomial.
(8 + x)(4 + x) = 0

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

Simplifying
8 + x = 0

Solving
8 + x = 0

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

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

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

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

Simplifying
x = -8
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-8, -4}