(x+5)(x+2)=4

Solution for (x+5)(x+2)=4 equation:

Simplifying
(x + 5)(x + 2) = 4

Reorder the terms:
(5 + x)(x + 2) = 4

Reorder the terms:
(5 + x)(2 + x) = 4

Multiply (5 + x) * (2 + x)
(5(2 + x) + x(2 + x)) = 4
((2 * 5 + x * 5) + x(2 + x)) = 4
((10 + 5x) + x(2 + x)) = 4
(10 + 5x + (2 * x + x * x)) = 4
(10 + 5x + (2x + x2)) = 4

Combine like terms: 5x + 2x = 7x
(10 + 7x + x2) = 4

Solving
10 + 7x + x2 = 4

Solving for variable 'x'.

Reorder the terms:
10 + -4 + 7x + x2 = 4 + -4

Combine like terms: 10 + -4 = 6
6 + 7x + x2 = 4 + -4

Combine like terms: 4 + -4 = 0
6 + 7x + x2 = 0

Factor a trinomial.
(6 + x)(1 + x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-6, -1}