8x(2+5x)-6=6x+4(2x-1)+4

Solution for 8x(2+5x)-6=6x+4(2x-1)+4 equation:

Simplifying
8x(2 + 5x) + -6 = 6x + 4(2x + -1) + 4
(2 * 8x + 5x * 8x) + -6 = 6x + 4(2x + -1) + 4
(16x + 40x2) + -6 = 6x + 4(2x + -1) + 4

Reorder the terms:
-6 + 16x + 40x2 = 6x + 4(2x + -1) + 4

Reorder the terms:
-6 + 16x + 40x2 = 6x + 4(-1 + 2x) + 4
-6 + 16x + 40x2 = 6x + (-1 * 4 + 2x * 4) + 4
-6 + 16x + 40x2 = 6x + (-4 + 8x) + 4

Reorder the terms:
-6 + 16x + 40x2 = -4 + 4 + 6x + 8x

Combine like terms: -4 + 4 = 0
-6 + 16x + 40x2 = 0 + 6x + 8x
-6 + 16x + 40x2 = 6x + 8x

Combine like terms: 6x + 8x = 14x
-6 + 16x + 40x2 = 14x

Solving
-6 + 16x + 40x2 = 14x

Solving for variable 'x'.

Reorder the terms:
-6 + 16x + -14x + 40x2 = 14x + -14x

Combine like terms: 16x + -14x = 2x
-6 + 2x + 40x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-6 + 2x + 40x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + x + 20x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + x + 20x2)' equal to zero and attempt to solve:

Simplifying
-3 + x + 20x2 = 0

Solving
-3 + x + 20x2 = 0

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

Divide each side by '20'.
-0.15 + 0.05x + x2 = 0.0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + 0.05x + 0.15 + x2 = 0.0 + 0.15

Reorder the terms:
-0.15 + 0.15 + 0.05x + x2 = 0.0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + 0.05x + x2 = 0.0 + 0.15
0.05x + x2 = 0.0 + 0.15

Combine like terms: 0.0 + 0.15 = 0.15
0.05x + x2 = 0.15

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.05x + 0.25 + x2 = 0.15 + 0.25

Reorder the terms:
0.25 + 0.05x + x2 = 0.15 + 0.25

Combine like terms: 0.15 + 0.25 = 0.4
0.25 + 0.05x + x2 = 0.4

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.632455532 and -0.632455532.

Subproblem 1
x + 0.5 = 0.632455532

Simplifying
x + 0.5 = 0.632455532

Reorder the terms:
0.5 + x = 0.632455532

Solving
0.5 + x = 0.632455532

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.632455532 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.632455532 + -0.5
x = 0.632455532 + -0.5

Combine like terms: 0.632455532 + -0.5 = 0.132455532
x = 0.132455532

Simplifying
x = 0.132455532

Subproblem 2
x + 0.5 = -0.632455532

Simplifying
x + 0.5 = -0.632455532

Reorder the terms:
0.5 + x = -0.632455532

Solving
0.5 + x = -0.632455532

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.632455532 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.632455532 + -0.5
x = -0.632455532 + -0.5

Combine like terms: -0.632455532 + -0.5 = -1.132455532
x = -1.132455532

Simplifying
x = -1.132455532

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.132455532, -1.132455532}
Solution
x = {0.132455532, -1.132455532}