x(3x-8)=180

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Solution for x(3x-8)=180 equation: 


Simplifying
x(3x + -8) = 180

Reorder the terms:
x(-8 + 3x) = 180
(-8 * x + 3x * x) = 180
(-8x + 3x2) = 180

Solving
-8x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + -8x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + -8x + 3x2 = 0

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

Divide each side by '3'.
-60 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -2.666666667x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -2.666666667x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -2.666666667x + x2 = 0 + 60
-2.666666667x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-2.666666667x + x2 = 60

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 60 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 60 + 1.777777780

Combine like terms: 60 + 1.777777780 = 61.77777778
1.777777780 + -2.666666667x + x2 = 61.77777778

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 61.77777778

Calculate the square root of the right side: 7.859884082

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 7.859884082 and -7.859884082.


Subproblem 1
x + -1.333333334 = 7.859884082

Simplifying
x + -1.333333334 = 7.859884082

Reorder the terms:
-1.333333334 + x = 7.859884082

Solving
-1.333333334 + x = 7.859884082

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 7.859884082 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 7.859884082 + 1.333333334
x = 7.859884082 + 1.333333334

Combine like terms: 7.859884082 + 1.333333334 = 9.193217416
x = 9.193217416

Simplifying
x = 9.193217416


Subproblem 2
x + -1.333333334 = -7.859884082

Simplifying
x + -1.333333334 = -7.859884082

Reorder the terms:
-1.333333334 + x = -7.859884082

Solving
-1.333333334 + x = -7.859884082

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -7.859884082 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -7.859884082 + 1.333333334
x = -7.859884082 + 1.333333334

Combine like terms: -7.859884082 + 1.333333334 = -6.526550748
x = -6.526550748

Simplifying
x = -6.526550748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.193217416, -6.526550748}

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