3x(2x+5)=8

Solution for 3x(2x+5)=8 equation:

Simplifying
3x(2x + 5) = 8

Reorder the terms:
3x(5 + 2x) = 8
(5 * 3x + 2x * 3x) = 8
(15x + 6x2) = 8

Solving
15x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 15x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 15x + 6x2 = 0

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

Divide each side by '6'.
-1.333333333 + 2.5x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 2.5x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 2.5x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 2.5x + x2 = 0 + 1.333333333
2.5x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
2.5x + x2 = 1.333333333

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 1.333333333 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 1.333333333 + 1.5625

Combine like terms: 1.333333333 + 1.5625 = 2.895833333
1.5625 + 2.5x + x2 = 2.895833333

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.895833333

Calculate the square root of the right side: 1.701714821

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.701714821 and -1.701714821.

Subproblem 1
x + 1.25 = 1.701714821

Simplifying
x + 1.25 = 1.701714821

Reorder the terms:
1.25 + x = 1.701714821

Solving
1.25 + x = 1.701714821

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.701714821 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.701714821 + -1.25
x = 1.701714821 + -1.25

Combine like terms: 1.701714821 + -1.25 = 0.451714821
x = 0.451714821

Simplifying
x = 0.451714821

Subproblem 2
x + 1.25 = -1.701714821

Simplifying
x + 1.25 = -1.701714821

Reorder the terms:
1.25 + x = -1.701714821

Solving
1.25 + x = -1.701714821

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.701714821 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.701714821 + -1.25
x = -1.701714821 + -1.25

Combine like terms: -1.701714821 + -1.25 = -2.951714821
x = -2.951714821

Simplifying
x = -2.951714821

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.451714821, -2.951714821}