(x-1)(x+4)x=0

Solution for (x-1)(x+4)x=0 equation:

Simplifying
(x + -1)(x + 4) * x = 0

Reorder the terms:
(-1 + x)(x + 4) * x = 0

Reorder the terms:
(-1 + x)(4 + x) * x = 0

Reorder the terms for easier multiplication:
x(-1 + x)(4 + x) = 0

Multiply (-1 + x) * (4 + x)
x(-1(4 + x) + x(4 + x)) = 0
x((4 * -1 + x * -1) + x(4 + x)) = 0
x((-4 + -1x) + x(4 + x)) = 0
x(-4 + -1x + (4 * x + x * x)) = 0
x(-4 + -1x + (4x + x2)) = 0

Combine like terms: -1x + 4x = 3x
x(-4 + 3x + x2) = 0
(-4 * x + 3x * x + x2 * x) = 0
(-4x + 3x2 + x3) = 0

Solving
-4x + 3x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + 3x + x2) = 0

Factor a trinomial.
x((-4 + -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 '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
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, -4, 1}