0=3x^4-30x^3+72x^2

Solution for 0=3x^4-30x^3+72x^2 equation:

Simplifying
0 = 3x4 + -30x3 + 72x2

Reorder the terms:
0 = 72x2 + -30x3 + 3x4

Solving
0 = 72x2 + -30x3 + 3x4

Solving for variable 'x'.
Remove the zero:
-72x2 + 30x3 + -3x4 = 72x2 + -30x3 + 3x4 + -72x2 + 30x3 + -3x4

Reorder the terms:
-72x2 + 30x3 + -3x4 = 72x2 + -72x2 + -30x3 + 30x3 + 3x4 + -3x4

Combine like terms: 72x2 + -72x2 = 0
-72x2 + 30x3 + -3x4 = 0 + -30x3 + 30x3 + 3x4 + -3x4
-72x2 + 30x3 + -3x4 = -30x3 + 30x3 + 3x4 + -3x4

Combine like terms: -30x3 + 30x3 = 0
-72x2 + 30x3 + -3x4 = 0 + 3x4 + -3x4
-72x2 + 30x3 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
-72x2 + 30x3 + -3x4 = 0

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(-24 + 10x + -1x2) = 0

Factor a trinomial.
3x2((-6 + x)(4 + -1x)) = 0

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, 6, 4}