10x-3x(x-6)=x+30

Solution for 10x-3x(x-6)=x+30 equation:

Simplifying
10x + -3x(x + -6) = x + 30

Reorder the terms:
10x + -3x(-6 + x) = x + 30
10x + (-6 * -3x + x * -3x) = x + 30
10x + (18x + -3x2) = x + 30

Combine like terms: 10x + 18x = 28x
28x + -3x2 = x + 30

Reorder the terms:
28x + -3x2 = 30 + x

Solving
28x + -3x2 = 30 + x

Solving for variable 'x'.

Reorder the terms:
-30 + 28x + -1x + -3x2 = 30 + x + -30 + -1x

Combine like terms: 28x + -1x = 27x
-30 + 27x + -3x2 = 30 + x + -30 + -1x

Reorder the terms:
-30 + 27x + -3x2 = 30 + -30 + x + -1x

Combine like terms: 30 + -30 = 0
-30 + 27x + -3x2 = 0 + x + -1x
-30 + 27x + -3x2 = x + -1x

Combine like terms: x + -1x = 0
-30 + 27x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 9x + -1x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-10 + 9x + -1x2)' equal to zero and attempt to solve:

Simplifying
-10 + 9x + -1x2 = 0

Solving
-10 + 9x + -1x2 = 0

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

Divide each side by '-1'.
10 + -9x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -9x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -9x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -9x + x2 = 0 + -10
-9x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-9x + x2 = -10

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 = -10 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -10 + 20.25

Combine like terms: -10 + 20.25 = 10.25
20.25 + -9x + x2 = 10.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
x + -4.5 = 3.201562119

Simplifying
x + -4.5 = 3.201562119

Reorder the terms:
-4.5 + x = 3.201562119

Solving
-4.5 + x = 3.201562119

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 = 3.201562119 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.201562119 + 4.5
x = 3.201562119 + 4.5

Combine like terms: 3.201562119 + 4.5 = 7.701562119
x = 7.701562119

Simplifying
x = 7.701562119

Subproblem 2
x + -4.5 = -3.201562119

Simplifying
x + -4.5 = -3.201562119

Reorder the terms:
-4.5 + x = -3.201562119

Solving
-4.5 + x = -3.201562119

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 = -3.201562119 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.201562119 + 4.5
x = -3.201562119 + 4.5

Combine like terms: -3.201562119 + 4.5 = 1.298437881
x = 1.298437881

Simplifying
x = 1.298437881

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.701562119, 1.298437881}
Solution
x = {7.701562119, 1.298437881}