9(b-4)7b=5(3b-2)

Solution for 9(b-4)7b=5(3b-2) equation:

Simplifying
9(b + -4) * 7b = 5(3b + -2)

Reorder the terms:
9(-4 + b) * 7b = 5(3b + -2)

Reorder the terms for easier multiplication:
9 * 7b(-4 + b) = 5(3b + -2)

Multiply 9 * 7
63b(-4 + b) = 5(3b + -2)
(-4 * 63b + b * 63b) = 5(3b + -2)
(-252b + 63b2) = 5(3b + -2)

Reorder the terms:
-252b + 63b2 = 5(-2 + 3b)
-252b + 63b2 = (-2 * 5 + 3b * 5)
-252b + 63b2 = (-10 + 15b)

Solving
-252b + 63b2 = -10 + 15b

Solving for variable 'b'.

Reorder the terms:
10 + -252b + -15b + 63b2 = -10 + 15b + 10 + -15b

Combine like terms: -252b + -15b = -267b
10 + -267b + 63b2 = -10 + 15b + 10 + -15b

Reorder the terms:
10 + -267b + 63b2 = -10 + 10 + 15b + -15b

Combine like terms: -10 + 10 = 0
10 + -267b + 63b2 = 0 + 15b + -15b
10 + -267b + 63b2 = 15b + -15b

Combine like terms: 15b + -15b = 0
10 + -267b + 63b2 = 0

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

Divide each side by '63'.
0.1587301587 + -4.238095238b + b2 = 0

Move the constant term to the right:

Add '-0.1587301587' to each side of the equation.
0.1587301587 + -4.238095238b + -0.1587301587 + b2 = 0 + -0.1587301587

Reorder the terms:
0.1587301587 + -0.1587301587 + -4.238095238b + b2 = 0 + -0.1587301587

Combine like terms: 0.1587301587 + -0.1587301587 = 0.0000000000
0.0000000000 + -4.238095238b + b2 = 0 + -0.1587301587
-4.238095238b + b2 = 0 + -0.1587301587

Combine like terms: 0 + -0.1587301587 = -0.1587301587
-4.238095238b + b2 = -0.1587301587

The b term is -4.238095238b.  Take half its coefficient (-2.119047619).
Square it (4.490362812) and add it to both sides.

Add '4.490362812' to each side of the equation.
-4.238095238b + 4.490362812 + b2 = -0.1587301587 + 4.490362812

Reorder the terms:
4.490362812 + -4.238095238b + b2 = -0.1587301587 + 4.490362812

Combine like terms: -0.1587301587 + 4.490362812 = 4.3316326533
4.490362812 + -4.238095238b + b2 = 4.3316326533

Factor a perfect square on the left side:
(b + -2.119047619)(b + -2.119047619) = 4.3316326533

Calculate the square root of the right side: 2.081257469

Break this problem into two subproblems by setting 
(b + -2.119047619) equal to 2.081257469 and -2.081257469.

Subproblem 1
b + -2.119047619 = 2.081257469

Simplifying
b + -2.119047619 = 2.081257469

Reorder the terms:
-2.119047619 + b = 2.081257469

Solving
-2.119047619 + b = 2.081257469

Solving for variable 'b'.

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

Add '2.119047619' to each side of the equation.
-2.119047619 + 2.119047619 + b = 2.081257469 + 2.119047619

Combine like terms: -2.119047619 + 2.119047619 = 0.000000000
0.000000000 + b = 2.081257469 + 2.119047619
b = 2.081257469 + 2.119047619

Combine like terms: 2.081257469 + 2.119047619 = 4.200305088
b = 4.200305088

Simplifying
b = 4.200305088

Subproblem 2
b + -2.119047619 = -2.081257469

Simplifying
b + -2.119047619 = -2.081257469

Reorder the terms:
-2.119047619 + b = -2.081257469

Solving
-2.119047619 + b = -2.081257469

Solving for variable 'b'.

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

Add '2.119047619' to each side of the equation.
-2.119047619 + 2.119047619 + b = -2.081257469 + 2.119047619

Combine like terms: -2.119047619 + 2.119047619 = 0.000000000
0.000000000 + b = -2.081257469 + 2.119047619
b = -2.081257469 + 2.119047619

Combine like terms: -2.081257469 + 2.119047619 = 0.03779015
b = 0.03779015

Simplifying
b = 0.03779015

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {4.200305088, 0.03779015}