(x+5)(x+2)=

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

Simplifying
(x + 5)(x + 2) = 0

Reorder the terms:
(5 + x)(x + 2) = 0

Reorder the terms:
(5 + x)(2 + x) = 0

Multiply (5 + x) * (2 + x)
(5(2 + x) + x(2 + x)) = 0
((2 * 5 + x * 5) + x(2 + x)) = 0
((10 + 5x) + x(2 + x)) = 0
(10 + 5x + (2 * x + x * x)) = 0
(10 + 5x + (2x + x2)) = 0

Combine like terms: 5x + 2x = 7x
(10 + 7x + x2) = 0

Solving
10 + 7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + x)(2 + x) = 0

Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-5, -2}