6x(8x-5)=40

Solution for 6x(8x-5)=40 equation:

Simplifying
6x(8x + -5) = 40

Reorder the terms:
6x(-5 + 8x) = 40
(-5 * 6x + 8x * 6x) = 40
(-30x + 48x2) = 40

Solving
-30x + 48x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + -30x + 48x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + -30x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -15x + 24x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20 + -15x + 24x2)' equal to zero and attempt to solve:

Simplifying
-20 + -15x + 24x2 = 0

Solving
-20 + -15x + 24x2 = 0

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

Divide each side by '24'.
-0.8333333333 + -0.625x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -0.625x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -0.625x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -0.625x + x2 = 0 + 0.8333333333
-0.625x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-0.625x + x2 = 0.8333333333

The x term is -0.625x.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625x + 0.09765625 + x2 = 0.8333333333 + 0.09765625

Reorder the terms:
0.09765625 + -0.625x + x2 = 0.8333333333 + 0.09765625

Combine like terms: 0.8333333333 + 0.09765625 = 0.9309895833
0.09765625 + -0.625x + x2 = 0.9309895833

Factor a perfect square on the left side:
(x + -0.3125)(x + -0.3125) = 0.9309895833

Calculate the square root of the right side: 0.964878015

Break this problem into two subproblems by setting 
(x + -0.3125) equal to 0.964878015 and -0.964878015.

Subproblem 1
x + -0.3125 = 0.964878015

Simplifying
x + -0.3125 = 0.964878015

Reorder the terms:
-0.3125 + x = 0.964878015

Solving
-0.3125 + x = 0.964878015

Solving for variable 'x'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + x = 0.964878015 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + x = 0.964878015 + 0.3125
x = 0.964878015 + 0.3125

Combine like terms: 0.964878015 + 0.3125 = 1.277378015
x = 1.277378015

Simplifying
x = 1.277378015

Subproblem 2
x + -0.3125 = -0.964878015

Simplifying
x + -0.3125 = -0.964878015

Reorder the terms:
-0.3125 + x = -0.964878015

Solving
-0.3125 + x = -0.964878015

Solving for variable 'x'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + x = -0.964878015 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + x = -0.964878015 + 0.3125
x = -0.964878015 + 0.3125

Combine like terms: -0.964878015 + 0.3125 = -0.652378015
x = -0.652378015

Simplifying
x = -0.652378015

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.277378015, -0.652378015}
Solution
x = {1.277378015, -0.652378015}