(x+5)(x+10)=6

Solution for (x+5)(x+10)=6 equation:

Simplifying
(x + 5)(x + 10) = 6

Reorder the terms:
(5 + x)(x + 10) = 6

Reorder the terms:
(5 + x)(10 + x) = 6

Multiply (5 + x) * (10 + x)
(5(10 + x) + x(10 + x)) = 6
((10 * 5 + x * 5) + x(10 + x)) = 6
((50 + 5x) + x(10 + x)) = 6
(50 + 5x + (10 * x + x * x)) = 6
(50 + 5x + (10x + x2)) = 6

Combine like terms: 5x + 10x = 15x
(50 + 15x + x2) = 6

Solving
50 + 15x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
50 + -6 + 15x + x2 = 6 + -6

Combine like terms: 50 + -6 = 44
44 + 15x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
44 + 15x + x2 = 0

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

Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
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 = {-11, -4}