9=8b(2b-3)

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Solution for 9=8b(2b-3) equation:


Simplifying
9 = 8b(2b + -3)

Reorder the terms:
9 = 8b(-3 + 2b)
9 = (-3 * 8b + 2b * 8b)
9 = (-24b + 16b2)

Solving
9 = -24b + 16b2

Solving for variable 'b'.

Reorder the terms:
9 + 24b + -16b2 = -24b + 24b + 16b2 + -16b2

Combine like terms: -24b + 24b = 0
9 + 24b + -16b2 = 0 + 16b2 + -16b2
9 + 24b + -16b2 = 16b2 + -16b2

Combine like terms: 16b2 + -16b2 = 0
9 + 24b + -16b2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.5625 + -1.5b + b2 = 0

Move the constant term to the right:

Add '0.5625' to each side of the equation.
-0.5625 + -1.5b + 0.5625 + b2 = 0 + 0.5625

Reorder the terms:
-0.5625 + 0.5625 + -1.5b + b2 = 0 + 0.5625

Combine like terms: -0.5625 + 0.5625 = 0.0000
0.0000 + -1.5b + b2 = 0 + 0.5625
-1.5b + b2 = 0 + 0.5625

Combine like terms: 0 + 0.5625 = 0.5625
-1.5b + b2 = 0.5625

The b term is -1.5b.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5b + 0.5625 + b2 = 0.5625 + 0.5625

Reorder the terms:
0.5625 + -1.5b + b2 = 0.5625 + 0.5625

Combine like terms: 0.5625 + 0.5625 = 1.125
0.5625 + -1.5b + b2 = 1.125

Factor a perfect square on the left side:
(b + -0.75)(b + -0.75) = 1.125

Calculate the square root of the right side: 1.060660172

Break this problem into two subproblems by setting 
(b + -0.75) equal to 1.060660172 and -1.060660172.

Subproblem 1

b + -0.75 = 1.060660172 Simplifying b + -0.75 = 1.060660172 Reorder the terms: -0.75 + b = 1.060660172 Solving -0.75 + b = 1.060660172 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + b = 1.060660172 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + b = 1.060660172 + 0.75 b = 1.060660172 + 0.75 Combine like terms: 1.060660172 + 0.75 = 1.810660172 b = 1.810660172 Simplifying b = 1.810660172

Subproblem 2

b + -0.75 = -1.060660172 Simplifying b + -0.75 = -1.060660172 Reorder the terms: -0.75 + b = -1.060660172 Solving -0.75 + b = -1.060660172 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + b = -1.060660172 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + b = -1.060660172 + 0.75 b = -1.060660172 + 0.75 Combine like terms: -1.060660172 + 0.75 = -0.310660172 b = -0.310660172 Simplifying b = -0.310660172

Solution

The solution to the problem is based on the solutions from the subproblems. b = {1.810660172, -0.310660172}

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