x(x+6)-5(x+6)=0

Solution for x(x+6)-5(x+6)=0 equation:

Simplifying
x(x + 6) + -5(x + 6) = 0

Reorder the terms:
x(6 + x) + -5(x + 6) = 0
(6 * x + x * x) + -5(x + 6) = 0
(6x + x2) + -5(x + 6) = 0

Reorder the terms:
6x + x2 + -5(6 + x) = 0
6x + x2 + (6 * -5 + x * -5) = 0
6x + x2 + (-30 + -5x) = 0

Reorder the terms:
-30 + 6x + -5x + x2 = 0

Combine like terms: 6x + -5x = 1x
-30 + 1x + x2 = 0

Solving
-30 + 1x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}