3x(x-3)+4x=5

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Solution for 3x(x-3)+4x=5 equation: 


Simplifying
3x(x + -3) + 4x = 5

Reorder the terms:
3x(-3 + x) + 4x = 5
(-3 * 3x + x * 3x) + 4x = 5
(-9x + 3x2) + 4x = 5

Reorder the terms:
-9x + 4x + 3x2 = 5

Combine like terms: -9x + 4x = -5x
-5x + 3x2 = 5

Solving
-5x + 3x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -5x + 3x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -5x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + -1.666666667x + x2 = 0

Move the constant term to the right:

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

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

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + 1.666666667
-1.666666667x + x2 = 0 + 1.666666667

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

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 = 1.666666667 + 0.6944444447

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

Combine like terms: 1.666666667 + 0.6944444447 = 2.3611111117
0.6944444447 + -1.666666667x + x2 = 2.3611111117

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 2.3611111117

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 1.536590743 and -1.536590743.


Subproblem 1
x + -0.8333333335 = 1.536590743

Simplifying
x + -0.8333333335 = 1.536590743

Reorder the terms:
-0.8333333335 + x = 1.536590743

Solving
-0.8333333335 + x = 1.536590743

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 = 1.536590743 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 1.536590743 + 0.8333333335
x = 1.536590743 + 0.8333333335

Combine like terms: 1.536590743 + 0.8333333335 = 2.3699240765
x = 2.3699240765

Simplifying
x = 2.3699240765


Subproblem 2
x + -0.8333333335 = -1.536590743

Simplifying
x + -0.8333333335 = -1.536590743

Reorder the terms:
-0.8333333335 + x = -1.536590743

Solving
-0.8333333335 + x = -1.536590743

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 = -1.536590743 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -1.536590743 + 0.8333333335
x = -1.536590743 + 0.8333333335

Combine like terms: -1.536590743 + 0.8333333335 = -0.7032574095
x = -0.7032574095

Simplifying
x = -0.7032574095


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.3699240765, -0.7032574095}

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