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

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

Simplifying
(x + -1)(x + 6) * x = 0

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

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

Reorder the terms for easier multiplication:
x(-1 + x)(6 + x) = 0

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

Combine like terms: -1x + 6x = 5x
x(-6 + 5x + x2) = 0
(-6 * x + 5x * x + x2 * x) = 0
(-6x + 5x2 + x3) = 0

Solving
-6x + 5x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + 5x + x2) = 0

Factor a trinomial.
x((-6 + -1x)(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 '(-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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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, -6, 1}