3(x-8)5x+6=

Solution for 3(x-8)5x+6= equation:

Simplifying
3(x + -8) * 5x + 6 = 0

Reorder the terms:
3(-8 + x) * 5x + 6 = 0

Reorder the terms for easier multiplication:
3 * 5x(-8 + x) + 6 = 0

Multiply 3 * 5
15x(-8 + x) + 6 = 0
(-8 * 15x + x * 15x) + 6 = 0
(-120x + 15x2) + 6 = 0

Reorder the terms:
6 + -120x + 15x2 = 0

Solving
6 + -120x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -40x + 5x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -40x + 5x2)' equal to zero and attempt to solve:

Simplifying
2 + -40x + 5x2 = 0

Solving
2 + -40x + 5x2 = 0

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

Divide each side by '5'.
0.4 + -8x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -8x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -8x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -8x + x2 = 0 + -0.4
-8x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-8x + x2 = -0.4

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -0.4 + 16

Reorder the terms:
16 + -8x + x2 = -0.4 + 16

Combine like terms: -0.4 + 16 = 15.6
16 + -8x + x2 = 15.6

Factor a perfect square on the left side:
(x + -4)(x + -4) = 15.6

Calculate the square root of the right side: 3.949683532

Break this problem into two subproblems by setting 
(x + -4) equal to 3.949683532 and -3.949683532.

Subproblem 1
x + -4 = 3.949683532

Simplifying
x + -4 = 3.949683532

Reorder the terms:
-4 + x = 3.949683532

Solving
-4 + x = 3.949683532

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.949683532 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.949683532 + 4
x = 3.949683532 + 4

Combine like terms: 3.949683532 + 4 = 7.949683532
x = 7.949683532

Simplifying
x = 7.949683532

Subproblem 2
x + -4 = -3.949683532

Simplifying
x + -4 = -3.949683532

Reorder the terms:
-4 + x = -3.949683532

Solving
-4 + x = -3.949683532

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.949683532 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.949683532 + 4
x = -3.949683532 + 4

Combine like terms: -3.949683532 + 4 = 0.050316468
x = 0.050316468

Simplifying
x = 0.050316468

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.949683532, 0.050316468}
Solution
x = {7.949683532, 0.050316468}