(x+6)(x+15)=0

Solution for (x+6)(x+15)=0 equation:

Simplifying
(x + 6)(x + 15) = 0

Reorder the terms:
(6 + x)(x + 15) = 0

Reorder the terms:
(6 + x)(15 + x) = 0

Multiply (6 + x) * (15 + x)
(6(15 + x) + x(15 + x)) = 0
((15 * 6 + x * 6) + x(15 + x)) = 0
((90 + 6x) + x(15 + x)) = 0
(90 + 6x + (15 * x + x * x)) = 0
(90 + 6x + (15x + x2)) = 0

Combine like terms: 6x + 15x = 21x
(90 + 21x + x2) = 0

Solving
90 + 21x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
15 + x = 0

Solving
15 + x = 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 + x = 0 + -15

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

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

Simplifying
x = -15
Subproblem 2
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
Solution
x = {-15, -6}