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

Solution for 3(x+7)(x+2)=0 equation:

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

Reorder the terms:
3(7 + x)(x + 2) = 0

Reorder the terms:
3(7 + x)(2 + x) = 0

Multiply (7 + x) * (2 + x)
3(7(2 + x) + x(2 + x)) = 0
3((2 * 7 + x * 7) + x(2 + x)) = 0
3((14 + 7x) + x(2 + x)) = 0
3(14 + 7x + (2 * x + x * x)) = 0
3(14 + 7x + (2x + x2)) = 0

Combine like terms: 7x + 2x = 9x
3(14 + 9x + x2) = 0
(14 * 3 + 9x * 3 + x2 * 3) = 0
(42 + 27x + 3x2) = 0

Solving
42 + 27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + 9x + x2) = 0

Factor a trinomial.
3((7 + x)(2 + x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
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 = {-7, -2}