(3x-30)(3x+3)-(2x-1)=0

Solution for (3x-30)(3x+3)-(2x-1)=0 equation:

Simplifying
(3x + -30)(3x + 3) + -1(2x + -1) = 0

Reorder the terms:
(-30 + 3x)(3x + 3) + -1(2x + -1) = 0

Reorder the terms:
(-30 + 3x)(3 + 3x) + -1(2x + -1) = 0

Multiply (-30 + 3x) * (3 + 3x)
(-30(3 + 3x) + 3x * (3 + 3x)) + -1(2x + -1) = 0
((3 * -30 + 3x * -30) + 3x * (3 + 3x)) + -1(2x + -1) = 0
((-90 + -90x) + 3x * (3 + 3x)) + -1(2x + -1) = 0
(-90 + -90x + (3 * 3x + 3x * 3x)) + -1(2x + -1) = 0
(-90 + -90x + (9x + 9x2)) + -1(2x + -1) = 0

Combine like terms: -90x + 9x = -81x
(-90 + -81x + 9x2) + -1(2x + -1) = 0

Reorder the terms:
-90 + -81x + 9x2 + -1(-1 + 2x) = 0
-90 + -81x + 9x2 + (-1 * -1 + 2x * -1) = 0
-90 + -81x + 9x2 + (1 + -2x) = 0

Reorder the terms:
-90 + 1 + -81x + -2x + 9x2 = 0

Combine like terms: -90 + 1 = -89
-89 + -81x + -2x + 9x2 = 0

Combine like terms: -81x + -2x = -83x
-89 + -83x + 9x2 = 0

Solving
-89 + -83x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-9.888888889 + -9.222222222x + x2 = 0

Move the constant term to the right:

Add '9.888888889' to each side of the equation.
-9.888888889 + -9.222222222x + 9.888888889 + x2 = 0 + 9.888888889

Reorder the terms:
-9.888888889 + 9.888888889 + -9.222222222x + x2 = 0 + 9.888888889

Combine like terms: -9.888888889 + 9.888888889 = 0.000000000
0.000000000 + -9.222222222x + x2 = 0 + 9.888888889
-9.222222222x + x2 = 0 + 9.888888889

Combine like terms: 0 + 9.888888889 = 9.888888889
-9.222222222x + x2 = 9.888888889

The x term is -9.222222222x.  Take half its coefficient (-4.611111111).
Square it (21.26234568) and add it to both sides.

Add '21.26234568' to each side of the equation.
-9.222222222x + 21.26234568 + x2 = 9.888888889 + 21.26234568

Reorder the terms:
21.26234568 + -9.222222222x + x2 = 9.888888889 + 21.26234568

Combine like terms: 9.888888889 + 21.26234568 = 31.151234569
21.26234568 + -9.222222222x + x2 = 31.151234569

Factor a perfect square on the left side:
(x + -4.611111111)(x + -4.611111111) = 31.151234569

Calculate the square root of the right side: 5.581329104

Break this problem into two subproblems by setting 
(x + -4.611111111) equal to 5.581329104 and -5.581329104.

Subproblem 1
x + -4.611111111 = 5.581329104

Simplifying
x + -4.611111111 = 5.581329104

Reorder the terms:
-4.611111111 + x = 5.581329104

Solving
-4.611111111 + x = 5.581329104

Solving for variable 'x'.

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

Add '4.611111111' to each side of the equation.
-4.611111111 + 4.611111111 + x = 5.581329104 + 4.611111111

Combine like terms: -4.611111111 + 4.611111111 = 0.000000000
0.000000000 + x = 5.581329104 + 4.611111111
x = 5.581329104 + 4.611111111

Combine like terms: 5.581329104 + 4.611111111 = 10.192440215
x = 10.192440215

Simplifying
x = 10.192440215

Subproblem 2
x + -4.611111111 = -5.581329104

Simplifying
x + -4.611111111 = -5.581329104

Reorder the terms:
-4.611111111 + x = -5.581329104

Solving
-4.611111111 + x = -5.581329104

Solving for variable 'x'.

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

Add '4.611111111' to each side of the equation.
-4.611111111 + 4.611111111 + x = -5.581329104 + 4.611111111

Combine like terms: -4.611111111 + 4.611111111 = 0.000000000
0.000000000 + x = -5.581329104 + 4.611111111
x = -5.581329104 + 4.611111111

Combine like terms: -5.581329104 + 4.611111111 = -0.970217993
x = -0.970217993

Simplifying
x = -0.970217993

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.192440215, -0.970217993}