(2x-1)(3x+4)=8

Solution for (2x-1)(3x+4)=8 equation:

Simplifying
(2x + -1)(3x + 4) = 8

Reorder the terms:
(-1 + 2x)(3x + 4) = 8

Reorder the terms:
(-1 + 2x)(4 + 3x) = 8

Multiply (-1 + 2x) * (4 + 3x)
(-1(4 + 3x) + 2x * (4 + 3x)) = 8
((4 * -1 + 3x * -1) + 2x * (4 + 3x)) = 8
((-4 + -3x) + 2x * (4 + 3x)) = 8
(-4 + -3x + (4 * 2x + 3x * 2x)) = 8
(-4 + -3x + (8x + 6x2)) = 8

Combine like terms: -3x + 8x = 5x
(-4 + 5x + 6x2) = 8

Solving
-4 + 5x + 6x2 = 8

Solving for variable 'x'.

Reorder the terms:
-4 + -8 + 5x + 6x2 = 8 + -8

Combine like terms: -4 + -8 = -12
-12 + 5x + 6x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-12 + 5x + 6x2 = 0

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

Divide each side by '6'.
-2 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.8333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.8333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.8333333333x + x2 = 0 + 2
0.8333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.8333333333x + x2 = 2

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = 2 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = 2 + 0.1736111111

Combine like terms: 2 + 0.1736111111 = 2.1736111111
0.1736111111 + 0.8333333333x + x2 = 2.1736111111

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 2.1736111111

Calculate the square root of the right side: 1.474317168

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 1.474317168 and -1.474317168.

Subproblem 1
x + 0.4166666667 = 1.474317168

Simplifying
x + 0.4166666667 = 1.474317168

Reorder the terms:
0.4166666667 + x = 1.474317168

Solving
0.4166666667 + x = 1.474317168

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = 1.474317168 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = 1.474317168 + -0.4166666667
x = 1.474317168 + -0.4166666667

Combine like terms: 1.474317168 + -0.4166666667 = 1.0576505013
x = 1.0576505013

Simplifying
x = 1.0576505013

Subproblem 2
x + 0.4166666667 = -1.474317168

Simplifying
x + 0.4166666667 = -1.474317168

Reorder the terms:
0.4166666667 + x = -1.474317168

Solving
0.4166666667 + x = -1.474317168

Solving for variable 'x'.

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

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -0.4166666667 + x = -1.474317168 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = -1.474317168 + -0.4166666667
x = -1.474317168 + -0.4166666667

Combine like terms: -1.474317168 + -0.4166666667 = -1.8909838347
x = -1.8909838347

Simplifying
x = -1.8909838347

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0576505013, -1.8909838347}