3x+3x(x-10)=330

Solution for 3x+3x(x-10)=330 equation:

Simplifying
3x + 3x(x + -10) = 330

Reorder the terms:
3x + 3x(-10 + x) = 330
3x + (-10 * 3x + x * 3x) = 330
3x + (-30x + 3x2) = 330

Combine like terms: 3x + -30x = -27x
-27x + 3x2 = 330

Solving
-27x + 3x2 = 330

Solving for variable 'x'.

Reorder the terms:
-330 + -27x + 3x2 = 330 + -330

Combine like terms: 330 + -330 = 0
-330 + -27x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-110 + -9x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-110 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
-110 + -9x + x2 = 0

Solving
-110 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '110' to each side of the equation.
-110 + -9x + 110 + x2 = 0 + 110

Reorder the terms:
-110 + 110 + -9x + x2 = 0 + 110

Combine like terms: -110 + 110 = 0
0 + -9x + x2 = 0 + 110
-9x + x2 = 0 + 110

Combine like terms: 0 + 110 = 110
-9x + x2 = 110

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 110 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 110 + 20.25

Combine like terms: 110 + 20.25 = 130.25
20.25 + -9x + x2 = 130.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 130.25

Calculate the square root of the right side: 11.412712211

Break this problem into two subproblems by setting 
(x + -4.5) equal to 11.412712211 and -11.412712211.

Subproblem 1
x + -4.5 = 11.412712211

Simplifying
x + -4.5 = 11.412712211

Reorder the terms:
-4.5 + x = 11.412712211

Solving
-4.5 + x = 11.412712211

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 11.412712211 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 11.412712211 + 4.5
x = 11.412712211 + 4.5

Combine like terms: 11.412712211 + 4.5 = 15.912712211
x = 15.912712211

Simplifying
x = 15.912712211

Subproblem 2
x + -4.5 = -11.412712211

Simplifying
x + -4.5 = -11.412712211

Reorder the terms:
-4.5 + x = -11.412712211

Solving
-4.5 + x = -11.412712211

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -11.412712211 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -11.412712211 + 4.5
x = -11.412712211 + 4.5

Combine like terms: -11.412712211 + 4.5 = -6.912712211
x = -6.912712211

Simplifying
x = -6.912712211

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.912712211, -6.912712211}
Solution
x = {15.912712211, -6.912712211}