2(3x-1)(2x+5)=5

Solution for 2(3x-1)(2x+5)=5 equation:

Simplifying
2(3x + -1)(2x + 5) = 5

Reorder the terms:
2(-1 + 3x)(2x + 5) = 5

Reorder the terms:
2(-1 + 3x)(5 + 2x) = 5

Multiply (-1 + 3x) * (5 + 2x)
2(-1(5 + 2x) + 3x * (5 + 2x)) = 5
2((5 * -1 + 2x * -1) + 3x * (5 + 2x)) = 5
2((-5 + -2x) + 3x * (5 + 2x)) = 5
2(-5 + -2x + (5 * 3x + 2x * 3x)) = 5
2(-5 + -2x + (15x + 6x2)) = 5

Combine like terms: -2x + 15x = 13x
2(-5 + 13x + 6x2) = 5
(-5 * 2 + 13x * 2 + 6x2 * 2) = 5
(-10 + 26x + 12x2) = 5

Solving
-10 + 26x + 12x2 = 5

Solving for variable 'x'.

Reorder the terms:
-10 + -5 + 26x + 12x2 = 5 + -5

Combine like terms: -10 + -5 = -15
-15 + 26x + 12x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-15 + 26x + 12x2 = 0

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

Divide each side by '12'.
-1.25 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2.166666667x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2.166666667x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2.166666667x + x2 = 0 + 1.25
2.166666667x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2.166666667x + x2 = 1.25

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 1.25 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 1.25 + 1.173611113

Combine like terms: 1.25 + 1.173611113 = 2.423611113
1.173611113 + 2.166666667x + x2 = 2.423611113

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 2.423611113

Calculate the square root of the right side: 1.556795142

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 1.556795142 and -1.556795142.

Subproblem 1
x + 1.083333334 = 1.556795142

Simplifying
x + 1.083333334 = 1.556795142

Reorder the terms:
1.083333334 + x = 1.556795142

Solving
1.083333334 + x = 1.556795142

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = 1.556795142 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = 1.556795142 + -1.083333334
x = 1.556795142 + -1.083333334

Combine like terms: 1.556795142 + -1.083333334 = 0.473461808
x = 0.473461808

Simplifying
x = 0.473461808

Subproblem 2
x + 1.083333334 = -1.556795142

Simplifying
x + 1.083333334 = -1.556795142

Reorder the terms:
1.083333334 + x = -1.556795142

Solving
1.083333334 + x = -1.556795142

Solving for variable 'x'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + x = -1.556795142 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + x = -1.556795142 + -1.083333334
x = -1.556795142 + -1.083333334

Combine like terms: -1.556795142 + -1.083333334 = -2.640128476
x = -2.640128476

Simplifying
x = -2.640128476

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.473461808, -2.640128476}