3x(-3x+5)=5

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Solution for 3x(-3x+5)=5 equation: 


Simplifying
3x(-3x + 5) = 5

Reorder the terms:
3x(5 + -3x) = 5
(5 * 3x + -3x * 3x) = 5
(15x + -9x2) = 5

Solving
15x + -9x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 15x + -9x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 15x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
0.5555555556 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.5555555556' to each side of the equation.
0.5555555556 + -1.666666667x + -0.5555555556 + x2 = 0 + -0.5555555556

Reorder the terms:
0.5555555556 + -0.5555555556 + -1.666666667x + x2 = 0 + -0.5555555556

Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000
0.0000000000 + -1.666666667x + x2 = 0 + -0.5555555556
-1.666666667x + x2 = 0 + -0.5555555556

Combine like terms: 0 + -0.5555555556 = -0.5555555556
-1.666666667x + x2 = -0.5555555556

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = -0.5555555556 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = -0.5555555556 + 0.6944444447

Combine like terms: -0.5555555556 + 0.6944444447 = 0.1388888891
0.6944444447 + -1.666666667x + x2 = 0.1388888891

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 0.1388888891

Calculate the square root of the right side: 0.372677997

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 0.372677997 and -0.372677997.


Subproblem 1
x + -0.8333333335 = 0.372677997

Simplifying
x + -0.8333333335 = 0.372677997

Reorder the terms:
-0.8333333335 + x = 0.372677997

Solving
-0.8333333335 + x = 0.372677997

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 0.372677997 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 0.372677997 + 0.8333333335
x = 0.372677997 + 0.8333333335

Combine like terms: 0.372677997 + 0.8333333335 = 1.2060113305
x = 1.2060113305

Simplifying
x = 1.2060113305


Subproblem 2
x + -0.8333333335 = -0.372677997

Simplifying
x + -0.8333333335 = -0.372677997

Reorder the terms:
-0.8333333335 + x = -0.372677997

Solving
-0.8333333335 + x = -0.372677997

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -0.372677997 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -0.372677997 + 0.8333333335
x = -0.372677997 + 0.8333333335

Combine like terms: -0.372677997 + 0.8333333335 = 0.4606553365
x = 0.4606553365

Simplifying
x = 0.4606553365


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.2060113305, 0.4606553365}

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