x(x^2-44x+84)=0

Solution for x(x^2-44x+84)=0 equation:

Simplifying
x(x2 + -44x + 84) = 0

Reorder the terms:
x(84 + -44x + x2) = 0
(84 * x + -44x * x + x2 * x) = 0
(84x + -44x2 + x3) = 0

Solving
84x + -44x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(84 + -44x + x2) = 0

Factor a trinomial.
x((2 + -1x)(42 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 3
Set the factor '(42 + -1x)' equal to zero and attempt to solve:

Simplifying
42 + -1x = 0

Solving
42 + -1x = 0

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

Add '-42' to each side of the equation.
42 + -42 + -1x = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1x = 0 + -42
-1x = 0 + -42

Combine like terms: 0 + -42 = -42
-1x = -42

Divide each side by '-1'.
x = 42

Simplifying
x = 42
Solution
x = {0, 2, 42}