2x(10xb-3x)=6xb(2xb-0)

Solution for 2x(10xb-3x)=6xb(2xb-0) equation:

Simplifying
2x(10xb + -3x) = 6xb(2xb + 0)
(10bx * 2x + -3x * 2x) = 6xb(2xb + 0)
(20bx2 + -6x2) = 6xb(2xb + 0)

Reorder the terms:
20bx2 + -6x2 = 6bx(0 + 2bx)
Remove the zero:
20bx2 + -6x2 = 6bx(2bx)

Remove parenthesis around (2bx)
20bx2 + -6x2 = 6bx * 2bx

Reorder the terms for easier multiplication:
20bx2 + -6x2 = 6 * 2bx * bx

Multiply 6 * 2
20bx2 + -6x2 = 12bx * bx

Multiply bx * bx
20bx2 + -6x2 = 12b2x2

Solving
20bx2 + -6x2 = 12b2x2

Solving for variable 'b'.

Reorder the terms:
20bx2 + -12b2x2 + -6x2 = 12b2x2 + -12b2x2

Combine like terms: 12b2x2 + -12b2x2 = 0
20bx2 + -12b2x2 + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(10b + -6b2 + -3) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 = 0 + -1x2
Remove the zero:
0 = -1x2

Simplifying
0 = -1x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(10b + -6b2 + -3)' equal to zero and attempt to solve:

Simplifying
10b + -6b2 + -3 = 0

Reorder the terms:
-3 + 10b + -6b2 = 0

Solving
-3 + 10b + -6b2 = 0

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

Divide each side by '-6'.
0.5 + -1.666666667b + b2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.666666667b + -0.5 + b2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.666666667b + b2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.666666667b + b2 = 0 + -0.5
-1.666666667b + b2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1.666666667b + b2 = -0.5

The b term is -1.666666667b.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667b + 0.6944444447 + b2 = -0.5 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667b + b2 = -0.5 + 0.6944444447

Combine like terms: -0.5 + 0.6944444447 = 0.1944444447
0.6944444447 + -1.666666667b + b2 = 0.1944444447

Factor a perfect square on the left side:
(b + -0.8333333335)(b + -0.8333333335) = 0.1944444447

Calculate the square root of the right side: 0.440958552

Break this problem into two subproblems by setting 
(b + -0.8333333335) equal to 0.440958552 and -0.440958552.

Subproblem 1
b + -0.8333333335 = 0.440958552

Simplifying
b + -0.8333333335 = 0.440958552

Reorder the terms:
-0.8333333335 + b = 0.440958552

Solving
-0.8333333335 + b = 0.440958552

Solving for variable 'b'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + b = 0.440958552 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + b = 0.440958552 + 0.8333333335
b = 0.440958552 + 0.8333333335

Combine like terms: 0.440958552 + 0.8333333335 = 1.2742918855
b = 1.2742918855

Simplifying
b = 1.2742918855

Subproblem 2
b + -0.8333333335 = -0.440958552

Simplifying
b + -0.8333333335 = -0.440958552

Reorder the terms:
-0.8333333335 + b = -0.440958552

Solving
-0.8333333335 + b = -0.440958552

Solving for variable 'b'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + b = -0.440958552 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + b = -0.440958552 + 0.8333333335
b = -0.440958552 + 0.8333333335

Combine like terms: -0.440958552 + 0.8333333335 = 0.3923747815
b = 0.3923747815

Simplifying
b = 0.3923747815

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {1.2742918855, 0.3923747815}
Solution
b = {1.2742918855, 0.3923747815}