X(x+6)(2x-1)=0

Solution for X(x+6)(2x-1)=0 equation:

Simplifying
X(x + 6)(2x + -1) = 0

Reorder the terms:
X(6 + x)(2x + -1) = 0

Reorder the terms:
X(6 + x)(-1 + 2x) = 0

Multiply (6 + x) * (-1 + 2x)
X(6(-1 + 2x) + x(-1 + 2x)) = 0
X((-1 * 6 + 2x * 6) + x(-1 + 2x)) = 0
X((-6 + 12x) + x(-1 + 2x)) = 0
X(-6 + 12x + (-1 * x + 2x * x)) = 0
X(-6 + 12x + (-1x + 2x2)) = 0

Combine like terms: 12x + -1x = 11x
X(-6 + 11x + 2x2) = 0
(-6 * X + 11x * X + 2x2 * X) = 0
(-6X + 11xX + 2x2X) = 0

Solving
-6X + 11xX + 2x2X = 0

Solving for variable 'X'.

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

Factor out the Greatest Common Factor (GCF), 'X'.
X(-6 + 11x + 2x2) = 0

Factor a trinomial.
X((-6 + -1x)(1 + -2x)) = 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 '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Add 'x' to each side of the equation.
-1x + x = 6 + x

Combine like terms: -1x + x = 0
0 = 6 + x

Simplifying
0 = 6 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
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

Add '2x' to each side of the equation.
-2x + 2x = -1 + 2x

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

Simplifying
0 = -1 + 2x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}