0=-3x^2+42x-72

Solution for 0=-3x^2+42x-72 equation:

Simplifying
0 = -3x2 + 42x + -72

Reorder the terms:
0 = -72 + 42x + -3x2

Solving
0 = -72 + 42x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + 72 = 72
72 + -42x + 3x2 = -72 + 42x + -3x2 + 72 + -42x + 3x2

Reorder the terms:
72 + -42x + 3x2 = -72 + 72 + 42x + -42x + -3x2 + 3x2

Combine like terms: -72 + 72 = 0
72 + -42x + 3x2 = 0 + 42x + -42x + -3x2 + 3x2
72 + -42x + 3x2 = 42x + -42x + -3x2 + 3x2

Combine like terms: 42x + -42x = 0
72 + -42x + 3x2 = 0 + -3x2 + 3x2
72 + -42x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
72 + -42x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + -14x + x2) = 0

Factor a trinomial.
3((2 + -1x)(12 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
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 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {2, 12}