(x+2)(2x+3)(2x)=

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

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

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

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

Remove parenthesis around (2x)
(2 + x)(3 + 2x) * 2x = 0

Reorder the terms for easier multiplication:
2x(2 + x)(3 + 2x) = 0

Multiply (2 + x) * (3 + 2x)
2x(2(3 + 2x) + x(3 + 2x)) = 0
2x((3 * 2 + 2x * 2) + x(3 + 2x)) = 0
2x((6 + 4x) + x(3 + 2x)) = 0
2x(6 + 4x + (3 * x + 2x * x)) = 0
2x(6 + 4x + (3x + 2x2)) = 0

Combine like terms: 4x + 3x = 7x
2x(6 + 7x + 2x2) = 0
(6 * 2x + 7x * 2x + 2x2 * 2x) = 0
(12x + 14x2 + 4x3) = 0

Solving
12x + 14x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(6 + 7x + 2x2) = 0

Factor a trinomial.
2x((2 + x)(3 + 2x)) = 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 '(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
Subproblem 3
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {0, -2, -1.5}