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

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


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

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

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

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

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

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

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

Multiply -1 * 2
-90 + -81x + 9x2 + -2(-1 + 2x) = 0
-90 + -81x + 9x2 + (-1 * -2 + 2x * -2) = 0
-90 + -81x + 9x2 + (2 + -4x) = 0

Reorder the terms:
-90 + 2 + -81x + -4x + 9x2 = 0

Combine like terms: -90 + 2 = -88
-88 + -81x + -4x + 9x2 = 0

Combine like terms: -81x + -4x = -85x
-88 + -85x + 9x2 = 0

Solving
-88 + -85x + 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'.
-9.777777778 + -9.444444444x + x2 = 0

Move the constant term to the right:

Add '9.777777778' to each side of the equation.
-9.777777778 + -9.444444444x + 9.777777778 + x2 = 0 + 9.777777778

Reorder the terms:
-9.777777778 + 9.777777778 + -9.444444444x + x2 = 0 + 9.777777778

Combine like terms: -9.777777778 + 9.777777778 = 0.000000000
0.000000000 + -9.444444444x + x2 = 0 + 9.777777778
-9.444444444x + x2 = 0 + 9.777777778

Combine like terms: 0 + 9.777777778 = 9.777777778
-9.444444444x + x2 = 9.777777778

The x term is -9.444444444x.  Take half its coefficient (-4.722222222).
Square it (22.29938271) and add it to both sides.

Add '22.29938271' to each side of the equation.
-9.444444444x + 22.29938271 + x2 = 9.777777778 + 22.29938271

Reorder the terms:
22.29938271 + -9.444444444x + x2 = 9.777777778 + 22.29938271

Combine like terms: 9.777777778 + 22.29938271 = 32.077160488
22.29938271 + -9.444444444x + x2 = 32.077160488

Factor a perfect square on the left side:
(x + -4.722222222)(x + -4.722222222) = 32.077160488

Calculate the square root of the right side: 5.663670231

Break this problem into two subproblems by setting 
(x + -4.722222222) equal to 5.663670231 and -5.663670231.


Subproblem 1
x + -4.722222222 = 5.663670231

Simplifying
x + -4.722222222 = 5.663670231

Reorder the terms:
-4.722222222 + x = 5.663670231

Solving
-4.722222222 + x = 5.663670231

Solving for variable 'x'.

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

Add '4.722222222' to each side of the equation.
-4.722222222 + 4.722222222 + x = 5.663670231 + 4.722222222

Combine like terms: -4.722222222 + 4.722222222 = 0.000000000
0.000000000 + x = 5.663670231 + 4.722222222
x = 5.663670231 + 4.722222222

Combine like terms: 5.663670231 + 4.722222222 = 10.385892453
x = 10.385892453

Simplifying
x = 10.385892453


Subproblem 2
x + -4.722222222 = -5.663670231

Simplifying
x + -4.722222222 = -5.663670231

Reorder the terms:
-4.722222222 + x = -5.663670231

Solving
-4.722222222 + x = -5.663670231

Solving for variable 'x'.

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

Add '4.722222222' to each side of the equation.
-4.722222222 + 4.722222222 + x = -5.663670231 + 4.722222222

Combine like terms: -4.722222222 + 4.722222222 = 0.000000000
0.000000000 + x = -5.663670231 + 4.722222222
x = -5.663670231 + 4.722222222

Combine like terms: -5.663670231 + 4.722222222 = -0.941448009
x = -0.941448009

Simplifying
x = -0.941448009


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.385892453, -0.941448009}

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