0=x^3-7x^2+12x

Solution for 0=x^3-7x^2+12x equation:

Simplifying
0 = x3 + -7x2 + 12x

Reorder the terms:
0 = 12x + -7x2 + x3

Solving
0 = 12x + -7x2 + x3

Solving for variable 'x'.
Remove the zero:
-12x + 7x2 + -1x3 = 12x + -7x2 + x3 + -12x + 7x2 + -1x3

Reorder the terms:
-12x + 7x2 + -1x3 = 12x + -12x + -7x2 + 7x2 + x3 + -1x3

Combine like terms: 12x + -12x = 0
-12x + 7x2 + -1x3 = 0 + -7x2 + 7x2 + x3 + -1x3
-12x + 7x2 + -1x3 = -7x2 + 7x2 + x3 + -1x3

Combine like terms: -7x2 + 7x2 = 0
-12x + 7x2 + -1x3 = 0 + x3 + -1x3
-12x + 7x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-12x + 7x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-12 + 7x + -1x2) = 0

Factor a trinomial.
x((-4 + x)(3 + -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 + 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
Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 4, 3}