(x+6)(-x-9)=0

Solution for (x+6)(-x-9)=0 equation:

Simplifying
(x + 6)(-1x + -9) = 0

Reorder the terms:
(6 + x)(-1x + -9) = 0

Reorder the terms:
(6 + x)(-9 + -1x) = 0

Multiply (6 + x) * (-9 + -1x)
(6(-9 + -1x) + x(-9 + -1x)) = 0
((-9 * 6 + -1x * 6) + x(-9 + -1x)) = 0
((-54 + -6x) + x(-9 + -1x)) = 0
(-54 + -6x + (-9 * x + -1x * x)) = 0
(-54 + -6x + (-9x + -1x2)) = 0

Combine like terms: -6x + -9x = -15x
(-54 + -15x + -1x2) = 0

Solving
-54 + -15x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(54 + 15x + x2) = 0

Factor a trinomial.
-1((9 + x)(6 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
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 = {-9, -6}