5x(3x+8)=4

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Solution for 5x(3x+8)=4 equation: 


Simplifying
5x(3x + 8) = 4

Reorder the terms:
5x(8 + 3x) = 4
(8 * 5x + 3x * 5x) = 4
(40x + 15x2) = 4

Solving
40x + 15x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + 40x + 15x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 40x + 15x2 = 0

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

Divide each side by '15'.
-0.2666666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '0.2666666667' to each side of the equation.
-0.2666666667 + 2.666666667x + 0.2666666667 + x2 = 0 + 0.2666666667

Reorder the terms:
-0.2666666667 + 0.2666666667 + 2.666666667x + x2 = 0 + 0.2666666667

Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000
0.0000000000 + 2.666666667x + x2 = 0 + 0.2666666667
2.666666667x + x2 = 0 + 0.2666666667

Combine like terms: 0 + 0.2666666667 = 0.2666666667
2.666666667x + x2 = 0.2666666667

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 = 0.2666666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 0.2666666667 + 1.777777780

Combine like terms: 0.2666666667 + 1.777777780 = 2.0444444467
1.777777780 + 2.666666667x + x2 = 2.0444444467

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 2.0444444467

Calculate the square root of the right side: 1.429840707

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.429840707 and -1.429840707.


Subproblem 1
x + 1.333333334 = 1.429840707

Simplifying
x + 1.333333334 = 1.429840707

Reorder the terms:
1.333333334 + x = 1.429840707

Solving
1.333333334 + x = 1.429840707

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 = 1.429840707 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 1.429840707 + -1.333333334
x = 1.429840707 + -1.333333334

Combine like terms: 1.429840707 + -1.333333334 = 0.096507373
x = 0.096507373

Simplifying
x = 0.096507373


Subproblem 2
x + 1.333333334 = -1.429840707

Simplifying
x + 1.333333334 = -1.429840707

Reorder the terms:
1.333333334 + x = -1.429840707

Solving
1.333333334 + x = -1.429840707

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 = -1.429840707 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -1.429840707 + -1.333333334
x = -1.429840707 + -1.333333334

Combine like terms: -1.429840707 + -1.333333334 = -2.763174041
x = -2.763174041

Simplifying
x = -2.763174041


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.096507373, -2.763174041}

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