7x(x+1)(2x)=0

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

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

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

Remove parenthesis around (2x)
7x(1 + x) * 2x = 0

Reorder the terms for easier multiplication:
7 * 2x * x(1 + x) = 0

Multiply 7 * 2
14x * x(1 + x) = 0

Multiply x * x
14x2(1 + x) = 0
(1 * 14x2 + x * 14x2) = 0
(14x2 + 14x3) = 0

Solving
14x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '14x2'.
14x2(1 + x) = 0

Ignore the factor 14.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0, -1}