2x(x-30)=30-(x-9)

Solution for 2x(x-30)=30-(x-9) equation:

Simplifying
2x(x + -30) = 30 + -1(x + -9)

Reorder the terms:
2x(-30 + x) = 30 + -1(x + -9)
(-30 * 2x + x * 2x) = 30 + -1(x + -9)
(-60x + 2x2) = 30 + -1(x + -9)

Reorder the terms:
-60x + 2x2 = 30 + -1(-9 + x)
-60x + 2x2 = 30 + (-9 * -1 + x * -1)
-60x + 2x2 = 30 + (9 + -1x)

Combine like terms: 30 + 9 = 39
-60x + 2x2 = 39 + -1x

Solving
-60x + 2x2 = 39 + -1x

Solving for variable 'x'.

Reorder the terms:
-39 + -60x + x + 2x2 = 39 + -1x + -39 + x

Combine like terms: -60x + x = -59x
-39 + -59x + 2x2 = 39 + -1x + -39 + x

Reorder the terms:
-39 + -59x + 2x2 = 39 + -39 + -1x + x

Combine like terms: 39 + -39 = 0
-39 + -59x + 2x2 = 0 + -1x + x
-39 + -59x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-39 + -59x + 2x2 = 0

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

Divide each side by '2'.
-19.5 + -29.5x + x2 = 0

Move the constant term to the right:

Add '19.5' to each side of the equation.
-19.5 + -29.5x + 19.5 + x2 = 0 + 19.5

Reorder the terms:
-19.5 + 19.5 + -29.5x + x2 = 0 + 19.5

Combine like terms: -19.5 + 19.5 = 0.0
0.0 + -29.5x + x2 = 0 + 19.5
-29.5x + x2 = 0 + 19.5

Combine like terms: 0 + 19.5 = 19.5
-29.5x + x2 = 19.5

The x term is -29.5x.  Take half its coefficient (-14.75).
Square it (217.5625) and add it to both sides.

Add '217.5625' to each side of the equation.
-29.5x + 217.5625 + x2 = 19.5 + 217.5625

Reorder the terms:
217.5625 + -29.5x + x2 = 19.5 + 217.5625

Combine like terms: 19.5 + 217.5625 = 237.0625
217.5625 + -29.5x + x2 = 237.0625

Factor a perfect square on the left side:
(x + -14.75)(x + -14.75) = 237.0625

Calculate the square root of the right side: 15.39683409

Break this problem into two subproblems by setting 
(x + -14.75) equal to 15.39683409 and -15.39683409.

Subproblem 1
x + -14.75 = 15.39683409

Simplifying
x + -14.75 = 15.39683409

Reorder the terms:
-14.75 + x = 15.39683409

Solving
-14.75 + x = 15.39683409

Solving for variable 'x'.

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

Add '14.75' to each side of the equation.
-14.75 + 14.75 + x = 15.39683409 + 14.75

Combine like terms: -14.75 + 14.75 = 0.00
0.00 + x = 15.39683409 + 14.75
x = 15.39683409 + 14.75

Combine like terms: 15.39683409 + 14.75 = 30.14683409
x = 30.14683409

Simplifying
x = 30.14683409

Subproblem 2
x + -14.75 = -15.39683409

Simplifying
x + -14.75 = -15.39683409

Reorder the terms:
-14.75 + x = -15.39683409

Solving
-14.75 + x = -15.39683409

Solving for variable 'x'.

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

Add '14.75' to each side of the equation.
-14.75 + 14.75 + x = -15.39683409 + 14.75

Combine like terms: -14.75 + 14.75 = 0.00
0.00 + x = -15.39683409 + 14.75
x = -15.39683409 + 14.75

Combine like terms: -15.39683409 + 14.75 = -0.64683409
x = -0.64683409

Simplifying
x = -0.64683409

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.14683409, -0.64683409}