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

Solution for 3(x+5)(2x+1)=0 equation:

Simplifying
3(x + 5)(2x + 1) = 0

Reorder the terms:
3(5 + x)(2x + 1) = 0

Reorder the terms:
3(5 + x)(1 + 2x) = 0

Multiply (5 + x) * (1 + 2x)
3(5(1 + 2x) + x(1 + 2x)) = 0
3((1 * 5 + 2x * 5) + x(1 + 2x)) = 0
3((5 + 10x) + x(1 + 2x)) = 0
3(5 + 10x + (1 * x + 2x * x)) = 0
3(5 + 10x + (1x + 2x2)) = 0

Combine like terms: 10x + 1x = 11x
3(5 + 11x + 2x2) = 0
(5 * 3 + 11x * 3 + 2x2 * 3) = 0
(15 + 33x + 6x2) = 0

Solving
15 + 33x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + 11x + 2x2) = 0

Factor a trinomial.
3((5 + x)(1 + 2x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-5, -0.5}