-3b(b-5)=-21

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Solution for -3b(b-5)=-21 equation: 


Simplifying
-3b(b + -5) = -21

Reorder the terms:
-3b(-5 + b) = -21
(-5 * -3b + b * -3b) = -21
(15b + -3b2) = -21

Solving
15b + -3b2 = -21

Solving for variable 'b'.

Reorder the terms:
21 + 15b + -3b2 = -21 + 21

Combine like terms: -21 + 21 = 0
21 + 15b + -3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 5b + -1b2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + 5b + -1b2)' equal to zero and attempt to solve:

Simplifying
7 + 5b + -1b2 = 0

Solving
7 + 5b + -1b2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + -5b + b2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -5b + 7 + b2 = 0 + 7

Reorder the terms:
-7 + 7 + -5b + b2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5b + b2 = 0 + 7
-5b + b2 = 0 + 7

Combine like terms: 0 + 7 = 7
-5b + b2 = 7

The b term is -5b.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5b + 6.25 + b2 = 7 + 6.25

Reorder the terms:
6.25 + -5b + b2 = 7 + 6.25

Combine like terms: 7 + 6.25 = 13.25
6.25 + -5b + b2 = 13.25

Factor a perfect square on the left side:
(b + -2.5)(b + -2.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(b + -2.5) equal to 3.640054945 and -3.640054945.


Subproblem 1
b + -2.5 = 3.640054945

Simplifying
b + -2.5 = 3.640054945

Reorder the terms:
-2.5 + b = 3.640054945

Solving
-2.5 + b = 3.640054945

Solving for variable 'b'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + b = 3.640054945 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + b = 3.640054945 + 2.5
b = 3.640054945 + 2.5

Combine like terms: 3.640054945 + 2.5 = 6.140054945
b = 6.140054945

Simplifying
b = 6.140054945


Subproblem 2
b + -2.5 = -3.640054945

Simplifying
b + -2.5 = -3.640054945

Reorder the terms:
-2.5 + b = -3.640054945

Solving
-2.5 + b = -3.640054945

Solving for variable 'b'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + b = -3.640054945 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + b = -3.640054945 + 2.5
b = -3.640054945 + 2.5

Combine like terms: -3.640054945 + 2.5 = -1.140054945
b = -1.140054945

Simplifying
b = -1.140054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {6.140054945, -1.140054945}
Solution
b = {6.140054945, -1.140054945}

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