-x^2(x-1)(x+4)=0

Solution for -x^2(x-1)(x+4)=0 equation:

Simplifying
-1x2(x + -1)(x + 4) = 0

Reorder the terms:
-1x2(-1 + x)(x + 4) = 0

Reorder the terms:
-1x2(-1 + x)(4 + x) = 0

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

Combine like terms: -1x + 4x = 3x
-1x2(-4 + 3x + x2) = 0
(-4 * -1x2 + 3x * -1x2 + x2 * -1x2) = 0
(4x2 + -3x3 + -1x4) = 0

Solving
4x2 + -3x3 + -1x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4 + -3x + -1x2) = 0

Factor a trinomial.
x2((1 + -1x)(4 + x)) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
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
Subproblem 3
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {0, 1, -4}