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

Solution for (5-x)(6+x)x=0 equation:

Simplifying
(5 + -1x)(6 + x) * x = 0

Reorder the terms for easier multiplication:
x(5 + -1x)(6 + x) = 0

Multiply (5 + -1x) * (6 + x)
x(5(6 + x) + -1x * (6 + x)) = 0
x((6 * 5 + x * 5) + -1x * (6 + x)) = 0
x((30 + 5x) + -1x * (6 + x)) = 0
x(30 + 5x + (6 * -1x + x * -1x)) = 0
x(30 + 5x + (-6x + -1x2)) = 0

Combine like terms: 5x + -6x = -1x
x(30 + -1x + -1x2) = 0
(30 * x + -1x * x + -1x2 * x) = 0
(30x + -1x2 + -1x3) = 0

Solving
30x + -1x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(30 + -1x + -1x2) = 0

Factor a trinomial.
x((5 + -1x)(6 + x)) = 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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 3
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {0, 5, -6}