x=(9x^2+7)(3)-(3x-5)(18x+7)

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Solution for x=(9x^2+7)(3)-(3x-5)(18x+7) equation: 


Simplifying
x = (9x2 + 7)(3) + -1(3x + -5)(18x + 7)

Reorder the terms:
x = (7 + 9x2)(3) + -1(3x + -5)(18x + 7)

Reorder the terms for easier multiplication:
x = 3(7 + 9x2) + -1(3x + -5)(18x + 7)
x = (7 * 3 + 9x2 * 3) + -1(3x + -5)(18x + 7)
x = (21 + 27x2) + -1(3x + -5)(18x + 7)

Reorder the terms:
x = 21 + 27x2 + -1(-5 + 3x)(18x + 7)

Reorder the terms:
x = 21 + 27x2 + -1(-5 + 3x)(7 + 18x)

Multiply (-5 + 3x) * (7 + 18x)
x = 21 + 27x2 + -1(-5(7 + 18x) + 3x * (7 + 18x))
x = 21 + 27x2 + -1((7 * -5 + 18x * -5) + 3x * (7 + 18x))
x = 21 + 27x2 + -1((-35 + -90x) + 3x * (7 + 18x))
x = 21 + 27x2 + -1(-35 + -90x + (7 * 3x + 18x * 3x))
x = 21 + 27x2 + -1(-35 + -90x + (21x + 54x2))

Combine like terms: -90x + 21x = -69x
x = 21 + 27x2 + -1(-35 + -69x + 54x2)
x = 21 + 27x2 + (-35 * -1 + -69x * -1 + 54x2 * -1)
x = 21 + 27x2 + (35 + 69x + -54x2)

Reorder the terms:
x = 21 + 35 + 69x + 27x2 + -54x2

Combine like terms: 21 + 35 = 56
x = 56 + 69x + 27x2 + -54x2

Combine like terms: 27x2 + -54x2 = -27x2
x = 56 + 69x + -27x2

Solving
x = 56 + 69x + -27x2

Solving for variable 'x'.

Reorder the terms:
-56 + x + -69x + 27x2 = 56 + 69x + -27x2 + -56 + -69x + 27x2

Combine like terms: x + -69x = -68x
-56 + -68x + 27x2 = 56 + 69x + -27x2 + -56 + -69x + 27x2

Reorder the terms:
-56 + -68x + 27x2 = 56 + -56 + 69x + -69x + -27x2 + 27x2

Combine like terms: 56 + -56 = 0
-56 + -68x + 27x2 = 0 + 69x + -69x + -27x2 + 27x2
-56 + -68x + 27x2 = 69x + -69x + -27x2 + 27x2

Combine like terms: 69x + -69x = 0
-56 + -68x + 27x2 = 0 + -27x2 + 27x2
-56 + -68x + 27x2 = -27x2 + 27x2

Combine like terms: -27x2 + 27x2 = 0
-56 + -68x + 27x2 = 0

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

Divide each side by '27'.
-2.074074074 + -2.518518519x + x2 = 0

Move the constant term to the right:

Add '2.074074074' to each side of the equation.
-2.074074074 + -2.518518519x + 2.074074074 + x2 = 0 + 2.074074074

Reorder the terms:
-2.074074074 + 2.074074074 + -2.518518519x + x2 = 0 + 2.074074074

Combine like terms: -2.074074074 + 2.074074074 = 0.000000000
0.000000000 + -2.518518519x + x2 = 0 + 2.074074074
-2.518518519x + x2 = 0 + 2.074074074

Combine like terms: 0 + 2.074074074 = 2.074074074
-2.518518519x + x2 = 2.074074074

The x term is -2.518518519x.  Take half its coefficient (-1.25925926).
Square it (1.585733884) and add it to both sides.

Add '1.585733884' to each side of the equation.
-2.518518519x + 1.585733884 + x2 = 2.074074074 + 1.585733884

Reorder the terms:
1.585733884 + -2.518518519x + x2 = 2.074074074 + 1.585733884

Combine like terms: 2.074074074 + 1.585733884 = 3.659807958
1.585733884 + -2.518518519x + x2 = 3.659807958

Factor a perfect square on the left side:
(x + -1.25925926)(x + -1.25925926) = 3.659807958

Calculate the square root of the right side: 1.913062455

Break this problem into two subproblems by setting 
(x + -1.25925926) equal to 1.913062455 and -1.913062455.


Subproblem 1
x + -1.25925926 = 1.913062455

Simplifying
x + -1.25925926 = 1.913062455

Reorder the terms:
-1.25925926 + x = 1.913062455

Solving
-1.25925926 + x = 1.913062455

Solving for variable 'x'.

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

Add '1.25925926' to each side of the equation.
-1.25925926 + 1.25925926 + x = 1.913062455 + 1.25925926

Combine like terms: -1.25925926 + 1.25925926 = 0.00000000
0.00000000 + x = 1.913062455 + 1.25925926
x = 1.913062455 + 1.25925926

Combine like terms: 1.913062455 + 1.25925926 = 3.172321715
x = 3.172321715

Simplifying
x = 3.172321715


Subproblem 2
x + -1.25925926 = -1.913062455

Simplifying
x + -1.25925926 = -1.913062455

Reorder the terms:
-1.25925926 + x = -1.913062455

Solving
-1.25925926 + x = -1.913062455

Solving for variable 'x'.

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

Add '1.25925926' to each side of the equation.
-1.25925926 + 1.25925926 + x = -1.913062455 + 1.25925926

Combine like terms: -1.25925926 + 1.25925926 = 0.00000000
0.00000000 + x = -1.913062455 + 1.25925926
x = -1.913062455 + 1.25925926

Combine like terms: -1.913062455 + 1.25925926 = -0.653803195
x = -0.653803195

Simplifying
x = -0.653803195


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.172321715, -0.653803195}

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