11x(12-x)-30=20x+59-6x(4x-13)

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Solution for 11x(12-x)-30=20x+59-6x(4x-13) equation: 


Simplifying
11x(12 + -1x) + -30 = 20x + 59 + -6x(4x + -13)
(12 * 11x + -1x * 11x) + -30 = 20x + 59 + -6x(4x + -13)
(132x + -11x2) + -30 = 20x + 59 + -6x(4x + -13)

Reorder the terms:
-30 + 132x + -11x2 = 20x + 59 + -6x(4x + -13)

Reorder the terms:
-30 + 132x + -11x2 = 20x + 59 + -6x(-13 + 4x)
-30 + 132x + -11x2 = 20x + 59 + (-13 * -6x + 4x * -6x)
-30 + 132x + -11x2 = 20x + 59 + (78x + -24x2)

Reorder the terms:
-30 + 132x + -11x2 = 59 + 20x + 78x + -24x2

Combine like terms: 20x + 78x = 98x
-30 + 132x + -11x2 = 59 + 98x + -24x2

Solving
-30 + 132x + -11x2 = 59 + 98x + -24x2

Solving for variable 'x'.

Reorder the terms:
-30 + -59 + 132x + -98x + -11x2 + 24x2 = 59 + 98x + -24x2 + -59 + -98x + 24x2

Combine like terms: -30 + -59 = -89
-89 + 132x + -98x + -11x2 + 24x2 = 59 + 98x + -24x2 + -59 + -98x + 24x2

Combine like terms: 132x + -98x = 34x
-89 + 34x + -11x2 + 24x2 = 59 + 98x + -24x2 + -59 + -98x + 24x2

Combine like terms: -11x2 + 24x2 = 13x2
-89 + 34x + 13x2 = 59 + 98x + -24x2 + -59 + -98x + 24x2

Reorder the terms:
-89 + 34x + 13x2 = 59 + -59 + 98x + -98x + -24x2 + 24x2

Combine like terms: 59 + -59 = 0
-89 + 34x + 13x2 = 0 + 98x + -98x + -24x2 + 24x2
-89 + 34x + 13x2 = 98x + -98x + -24x2 + 24x2

Combine like terms: 98x + -98x = 0
-89 + 34x + 13x2 = 0 + -24x2 + 24x2
-89 + 34x + 13x2 = -24x2 + 24x2

Combine like terms: -24x2 + 24x2 = 0
-89 + 34x + 13x2 = 0

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

Divide each side by '13'.
-6.846153846 + 2.615384615x + x2 = 0

Move the constant term to the right:

Add '6.846153846' to each side of the equation.
-6.846153846 + 2.615384615x + 6.846153846 + x2 = 0 + 6.846153846

Reorder the terms:
-6.846153846 + 6.846153846 + 2.615384615x + x2 = 0 + 6.846153846

Combine like terms: -6.846153846 + 6.846153846 = 0.000000000
0.000000000 + 2.615384615x + x2 = 0 + 6.846153846
2.615384615x + x2 = 0 + 6.846153846

Combine like terms: 0 + 6.846153846 = 6.846153846
2.615384615x + x2 = 6.846153846

The x term is 2.615384615x.  Take half its coefficient (1.307692308).
Square it (1.710059172) and add it to both sides.

Add '1.710059172' to each side of the equation.
2.615384615x + 1.710059172 + x2 = 6.846153846 + 1.710059172

Reorder the terms:
1.710059172 + 2.615384615x + x2 = 6.846153846 + 1.710059172

Combine like terms: 6.846153846 + 1.710059172 = 8.556213018
1.710059172 + 2.615384615x + x2 = 8.556213018

Factor a perfect square on the left side:
(x + 1.307692308)(x + 1.307692308) = 8.556213018

Calculate the square root of the right side: 2.925100514

Break this problem into two subproblems by setting 
(x + 1.307692308) equal to 2.925100514 and -2.925100514.


Subproblem 1
x + 1.307692308 = 2.925100514

Simplifying
x + 1.307692308 = 2.925100514

Reorder the terms:
1.307692308 + x = 2.925100514

Solving
1.307692308 + x = 2.925100514

Solving for variable 'x'.

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

Add '-1.307692308' to each side of the equation.
1.307692308 + -1.307692308 + x = 2.925100514 + -1.307692308

Combine like terms: 1.307692308 + -1.307692308 = 0.000000000
0.000000000 + x = 2.925100514 + -1.307692308
x = 2.925100514 + -1.307692308

Combine like terms: 2.925100514 + -1.307692308 = 1.617408206
x = 1.617408206

Simplifying
x = 1.617408206


Subproblem 2
x + 1.307692308 = -2.925100514

Simplifying
x + 1.307692308 = -2.925100514

Reorder the terms:
1.307692308 + x = -2.925100514

Solving
1.307692308 + x = -2.925100514

Solving for variable 'x'.

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

Add '-1.307692308' to each side of the equation.
1.307692308 + -1.307692308 + x = -2.925100514 + -1.307692308

Combine like terms: 1.307692308 + -1.307692308 = 0.000000000
0.000000000 + x = -2.925100514 + -1.307692308
x = -2.925100514 + -1.307692308

Combine like terms: -2.925100514 + -1.307692308 = -4.232792822
x = -4.232792822

Simplifying
x = -4.232792822


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.617408206, -4.232792822}

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