6(x+1)5(2x+6)=0

Solution for 6(x+1)5(2x+6)=0 equation:

Simplifying
6(x + 1) * 5(2x + 6) = 0

Reorder the terms:
6(1 + x) * 5(2x + 6) = 0

Reorder the terms:
6(1 + x) * 5(6 + 2x) = 0

Reorder the terms for easier multiplication:
6 * 5(1 + x)(6 + 2x) = 0

Multiply 6 * 5
30(1 + x)(6 + 2x) = 0

Multiply (1 + x) * (6 + 2x)
30(1(6 + 2x) + x(6 + 2x)) = 0
30((6 * 1 + 2x * 1) + x(6 + 2x)) = 0
30((6 + 2x) + x(6 + 2x)) = 0
30(6 + 2x + (6 * x + 2x * x)) = 0
30(6 + 2x + (6x + 2x2)) = 0

Combine like terms: 2x + 6x = 8x
30(6 + 8x + 2x2) = 0
(6 * 30 + 8x * 30 + 2x2 * 30) = 0
(180 + 240x + 60x2) = 0

Solving
180 + 240x + 60x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '60'.
60(3 + 4x + x2) = 0

Factor a trinomial.
60((3 + x)(1 + x)) = 0

Ignore the factor 60.
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 '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {-3, -1}