0=3x^2-24x+36

Solution for 0=3x^2-24x+36 equation:

Simplifying
0 = 3x2 + -24x + 36

Reorder the terms:
0 = 36 + -24x + 3x2

Solving
0 = 36 + -24x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -36 = -36
-36 + 24x + -3x2 = 36 + -24x + 3x2 + -36 + 24x + -3x2

Reorder the terms:
-36 + 24x + -3x2 = 36 + -36 + -24x + 24x + 3x2 + -3x2

Combine like terms: 36 + -36 = 0
-36 + 24x + -3x2 = 0 + -24x + 24x + 3x2 + -3x2
-36 + 24x + -3x2 = -24x + 24x + 3x2 + -3x2

Combine like terms: -24x + 24x = 0
-36 + 24x + -3x2 = 0 + 3x2 + -3x2
-36 + 24x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-36 + 24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + 8x + -1x2) = 0

Factor a trinomial.
3((-6 + x)(2 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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 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
Solution
x = {6, 2}