4(2b^2-3b+5)-3[2(b^2+5b-6)-3(2b^2-3b+1)]=0

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Solution for 4(2b^2-3b+5)-3[2(b^2+5b-6)-3(2b^2-3b+1)]=0 equation: 


Simplifying
4(2b2 + -3b + 5) + -3[2(b2 + 5b + -6) + -3(2b2 + -3b + 1)] = 0

Reorder the terms:
4(5 + -3b + 2b2) + -3[2(b2 + 5b + -6) + -3(2b2 + -3b + 1)] = 0
(5 * 4 + -3b * 4 + 2b2 * 4) + -3[2(b2 + 5b + -6) + -3(2b2 + -3b + 1)] = 0
(20 + -12b + 8b2) + -3[2(b2 + 5b + -6) + -3(2b2 + -3b + 1)] = 0

Reorder the terms:
20 + -12b + 8b2 + -3[2(-6 + 5b + b2) + -3(2b2 + -3b + 1)] = 0
20 + -12b + 8b2 + -3[(-6 * 2 + 5b * 2 + b2 * 2) + -3(2b2 + -3b + 1)] = 0
20 + -12b + 8b2 + -3[(-12 + 10b + 2b2) + -3(2b2 + -3b + 1)] = 0

Reorder the terms:
20 + -12b + 8b2 + -3[-12 + 10b + 2b2 + -3(1 + -3b + 2b2)] = 0
20 + -12b + 8b2 + -3[-12 + 10b + 2b2 + (1 * -3 + -3b * -3 + 2b2 * -3)] = 0
20 + -12b + 8b2 + -3[-12 + 10b + 2b2 + (-3 + 9b + -6b2)] = 0

Reorder the terms:
20 + -12b + 8b2 + -3[-12 + -3 + 10b + 9b + 2b2 + -6b2] = 0

Combine like terms: -12 + -3 = -15
20 + -12b + 8b2 + -3[-15 + 10b + 9b + 2b2 + -6b2] = 0

Combine like terms: 10b + 9b = 19b
20 + -12b + 8b2 + -3[-15 + 19b + 2b2 + -6b2] = 0

Combine like terms: 2b2 + -6b2 = -4b2
20 + -12b + 8b2 + -3[-15 + 19b + -4b2] = 0
20 + -12b + 8b2 + [-15 * -3 + 19b * -3 + -4b2 * -3] = 0
20 + -12b + 8b2 + [45 + -57b + 12b2] = 0

Reorder the terms:
20 + 45 + -12b + -57b + 8b2 + 12b2 = 0

Combine like terms: 20 + 45 = 65
65 + -12b + -57b + 8b2 + 12b2 = 0

Combine like terms: -12b + -57b = -69b
65 + -69b + 8b2 + 12b2 = 0

Combine like terms: 8b2 + 12b2 = 20b2
65 + -69b + 20b2 = 0

Solving
65 + -69b + 20b2 = 0

Solving for variable 'b'.

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

Divide each side by '20'.
3.25 + -3.45b + b2 = 0.0

Move the constant term to the right:

Add '-3.25' to each side of the equation.
3.25 + -3.45b + -3.25 + b2 = 0.0 + -3.25

Reorder the terms:
3.25 + -3.25 + -3.45b + b2 = 0.0 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + -3.45b + b2 = 0.0 + -3.25
-3.45b + b2 = 0.0 + -3.25

Combine like terms: 0.0 + -3.25 = -3.25
-3.45b + b2 = -3.25

The b term is -3.45b.  Take half its coefficient (-1.725).
Square it (2.975625) and add it to both sides.

Add '2.975625' to each side of the equation.
-3.45b + 2.975625 + b2 = -3.25 + 2.975625

Reorder the terms:
2.975625 + -3.45b + b2 = -3.25 + 2.975625

Combine like terms: -3.25 + 2.975625 = -0.274375
2.975625 + -3.45b + b2 = -0.274375

Factor a perfect square on the left side:
(b + -1.725)(b + -1.725) = -0.274375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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