-x(5+x)=6

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

Simplifying
-1x(5 + x) = 6
(5 * -1x + x * -1x) = 6
(-5x + -1x2) = 6

Solving
-5x + -1x2 = 6

Solving for variable 'x'.

Reorder the terms:
-6 + -5x + -1x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -5x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5x + x2) = 0

Factor a trinomial.
-1((3 + x)(2 + x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
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 = {-3, -2}