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

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

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

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

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

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

Combine like terms: 3x + -2x = 1x
x(-3 + 1x + 2x2) = 0
(-3 * x + 1x * x + 2x2 * x) = 0
(-3x + 1x2 + 2x3) = 0

Solving
-3x + 1x2 + 2x3 = 0

Solving for variable 'x'.

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

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {0, -1.5, 1}