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

Solution for x(x+1)-6(x+1)=0 equation:

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

Reorder the terms:
x(1 + x) + -6(x + 1) = 0
(1 * x + x * x) + -6(x + 1) = 0
(1x + x2) + -6(x + 1) = 0

Reorder the terms:
1x + x2 + -6(1 + x) = 0
1x + x2 + (1 * -6 + x * -6) = 0
1x + x2 + (-6 + -6x) = 0

Reorder the terms:
-6 + 1x + -6x + x2 = 0

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

Solving
-6 + -5x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
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
Solution
x = {-1, 6}