0=3x^2-225x+72

Solution for 0=3x^2-225x+72 equation:

Simplifying
0 = 3x2 + -225x + 72

Reorder the terms:
0 = 72 + -225x + 3x2

Solving
0 = 72 + -225x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -72 = -72
-72 + 225x + -3x2 = 72 + -225x + 3x2 + -72 + 225x + -3x2

Reorder the terms:
-72 + 225x + -3x2 = 72 + -72 + -225x + 225x + 3x2 + -3x2

Combine like terms: 72 + -72 = 0
-72 + 225x + -3x2 = 0 + -225x + 225x + 3x2 + -3x2
-72 + 225x + -3x2 = -225x + 225x + 3x2 + -3x2

Combine like terms: -225x + 225x = 0
-72 + 225x + -3x2 = 0 + 3x2 + -3x2
-72 + 225x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-72 + 225x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 75x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-24 + 75x + -1x2)' equal to zero and attempt to solve:

Simplifying
-24 + 75x + -1x2 = 0

Solving
-24 + 75x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
24 + -75x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -75x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -75x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -75x + x2 = 0 + -24
-75x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-75x + x2 = -24

The x term is -75x.  Take half its coefficient (-37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
-75x + 1406.25 + x2 = -24 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = -24 + 1406.25

Combine like terms: -24 + 1406.25 = 1382.25
1406.25 + -75x + x2 = 1382.25

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 1382.25

Calculate the square root of the right side: 37.17862289

Break this problem into two subproblems by setting 
(x + -37.5) equal to 37.17862289 and -37.17862289.

Subproblem 1
x + -37.5 = 37.17862289

Simplifying
x + -37.5 = 37.17862289

Reorder the terms:
-37.5 + x = 37.17862289

Solving
-37.5 + x = 37.17862289

Solving for variable 'x'.

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

Add '37.5' to each side of the equation.
-37.5 + 37.5 + x = 37.17862289 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x = 37.17862289 + 37.5
x = 37.17862289 + 37.5

Combine like terms: 37.17862289 + 37.5 = 74.67862289
x = 74.67862289

Simplifying
x = 74.67862289

Subproblem 2
x + -37.5 = -37.17862289

Simplifying
x + -37.5 = -37.17862289

Reorder the terms:
-37.5 + x = -37.17862289

Solving
-37.5 + x = -37.17862289

Solving for variable 'x'.

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

Add '37.5' to each side of the equation.
-37.5 + 37.5 + x = -37.17862289 + 37.5

Combine like terms: -37.5 + 37.5 = 0.0
0.0 + x = -37.17862289 + 37.5
x = -37.17862289 + 37.5

Combine like terms: -37.17862289 + 37.5 = 0.32137711
x = 0.32137711

Simplifying
x = 0.32137711

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {74.67862289, 0.32137711}
Solution
x = {74.67862289, 0.32137711}