7(x+2)(2x+6)=0

Solution for 7(x+2)(2x+6)=0 equation:

Simplifying
7(x + 2)(2x + 6) = 0

Reorder the terms:
7(2 + x)(2x + 6) = 0

Reorder the terms:
7(2 + x)(6 + 2x) = 0

Multiply (2 + x) * (6 + 2x)
7(2(6 + 2x) + x(6 + 2x)) = 0
7((6 * 2 + 2x * 2) + x(6 + 2x)) = 0
7((12 + 4x) + x(6 + 2x)) = 0
7(12 + 4x + (6 * x + 2x * x)) = 0
7(12 + 4x + (6x + 2x2)) = 0

Combine like terms: 4x + 6x = 10x
7(12 + 10x + 2x2) = 0
(12 * 7 + 10x * 7 + 2x2 * 7) = 0
(84 + 70x + 14x2) = 0

Solving
84 + 70x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14'.
14(6 + 5x + x2) = 0

Factor a trinomial.
14((3 + x)(2 + x)) = 0

Ignore the factor 14.
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}