x(x+6)(26-x)=0

Solution for x(x+6)(26-x)=0 equation:

Simplifying
x(x + 6)(26 + -1x) = 0

Reorder the terms:
x(6 + x)(26 + -1x) = 0

Multiply (6 + x) * (26 + -1x)
x(6(26 + -1x) + x(26 + -1x)) = 0
x((26 * 6 + -1x * 6) + x(26 + -1x)) = 0
x((156 + -6x) + x(26 + -1x)) = 0
x(156 + -6x + (26 * x + -1x * x)) = 0
x(156 + -6x + (26x + -1x2)) = 0

Combine like terms: -6x + 26x = 20x
x(156 + 20x + -1x2) = 0
(156 * x + 20x * x + -1x2 * x) = 0
(156x + 20x2 + -1x3) = 0

Solving
156x + 20x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(156 + 20x + -1x2) = 0

Factor a trinomial.
x((26 + -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 '(26 + -1x)' equal to zero and attempt to solve:

Simplifying
26 + -1x = 0

Solving
26 + -1x = 0

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

Add '-26' to each side of the equation.
26 + -26 + -1x = 0 + -26

Combine like terms: 26 + -26 = 0
0 + -1x = 0 + -26
-1x = 0 + -26

Combine like terms: 0 + -26 = -26
-1x = -26

Divide each side by '-1'.
x = 26

Simplifying
x = 26
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, 26, -6}