2x*(3-x)*(7x+1)=0

Solution for 2x*(3-x)*(7x+1)=0 equation:

Simplifying
2x(3 + -1x)(7x + 1) = 0

Reorder the terms:
2x(3 + -1x)(1 + 7x) = 0

Multiply (3 + -1x) * (1 + 7x)
2x(3(1 + 7x) + -1x * (1 + 7x)) = 0
2x((1 * 3 + 7x * 3) + -1x * (1 + 7x)) = 0
2x((3 + 21x) + -1x * (1 + 7x)) = 0
2x(3 + 21x + (1 * -1x + 7x * -1x)) = 0
2x(3 + 21x + (-1x + -7x2)) = 0

Combine like terms: 21x + -1x = 20x
2x(3 + 20x + -7x2) = 0
(3 * 2x + 20x * 2x + -7x2 * 2x) = 0
(6x + 40x2 + -14x3) = 0

Solving
6x + 40x2 + -14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(3 + 20x + -7x2) = 0

Factor a trinomial.
2x((3 + -1x)(1 + 7x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 3
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 = {0, 3, -0.1428571429}