(x+3)(21x+3)=0

Solution for (x+3)(21x+3)=0 equation:

Simplifying
(x + 3)(21x + 3) = 0

Reorder the terms:
(3 + x)(21x + 3) = 0

Reorder the terms:
(3 + x)(3 + 21x) = 0

Multiply (3 + x) * (3 + 21x)
(3(3 + 21x) + x(3 + 21x)) = 0
((3 * 3 + 21x * 3) + x(3 + 21x)) = 0
((9 + 63x) + x(3 + 21x)) = 0
(9 + 63x + (3 * x + 21x * x)) = 0
(9 + 63x + (3x + 21x2)) = 0

Combine like terms: 63x + 3x = 66x
(9 + 66x + 21x2) = 0

Solving
9 + 66x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 22x + 7x2) = 0

Factor a trinomial.
3((3 + x)(1 + 7x)) = 0

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

Simplifying
1 + 7x = 0

Solving
1 + 7x = 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 + 7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7x = 0 + -1
7x = 0 + -1

Combine like terms: 0 + -1 = -1
7x = -1

Divide each side by '7'.
x = -0.1428571429

Simplifying
x = -0.1428571429
Solution
x = {-3, -0.1428571429}