(4b+5)(3b-1)=(6b+1)(2b+1)

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


Simplifying
(4b + 5)(3b + -1) = (6b + 1)(2b + 1)

Reorder the terms:
(5 + 4b)(3b + -1) = (6b + 1)(2b + 1)

Reorder the terms:
(5 + 4b)(-1 + 3b) = (6b + 1)(2b + 1)

Multiply (5 + 4b) * (-1 + 3b)
(5(-1 + 3b) + 4b * (-1 + 3b)) = (6b + 1)(2b + 1)
((-1 * 5 + 3b * 5) + 4b * (-1 + 3b)) = (6b + 1)(2b + 1)
((-5 + 15b) + 4b * (-1 + 3b)) = (6b + 1)(2b + 1)
(-5 + 15b + (-1 * 4b + 3b * 4b)) = (6b + 1)(2b + 1)
(-5 + 15b + (-4b + 12b2)) = (6b + 1)(2b + 1)

Combine like terms: 15b + -4b = 11b
(-5 + 11b + 12b2) = (6b + 1)(2b + 1)

Reorder the terms:
-5 + 11b + 12b2 = (1 + 6b)(2b + 1)

Reorder the terms:
-5 + 11b + 12b2 = (1 + 6b)(1 + 2b)

Multiply (1 + 6b) * (1 + 2b)
-5 + 11b + 12b2 = (1(1 + 2b) + 6b * (1 + 2b))
-5 + 11b + 12b2 = ((1 * 1 + 2b * 1) + 6b * (1 + 2b))
-5 + 11b + 12b2 = ((1 + 2b) + 6b * (1 + 2b))
-5 + 11b + 12b2 = (1 + 2b + (1 * 6b + 2b * 6b))
-5 + 11b + 12b2 = (1 + 2b + (6b + 12b2))

Combine like terms: 2b + 6b = 8b
-5 + 11b + 12b2 = (1 + 8b + 12b2)

Add '-12b2' to each side of the equation.
-5 + 11b + 12b2 + -12b2 = 1 + 8b + 12b2 + -12b2

Combine like terms: 12b2 + -12b2 = 0
-5 + 11b + 0 = 1 + 8b + 12b2 + -12b2
-5 + 11b = 1 + 8b + 12b2 + -12b2

Combine like terms: 12b2 + -12b2 = 0
-5 + 11b = 1 + 8b + 0
-5 + 11b = 1 + 8b

Solving
-5 + 11b = 1 + 8b

Solving for variable 'b'.

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

Add '-8b' to each side of the equation.
-5 + 11b + -8b = 1 + 8b + -8b

Combine like terms: 11b + -8b = 3b
-5 + 3b = 1 + 8b + -8b

Combine like terms: 8b + -8b = 0
-5 + 3b = 1 + 0
-5 + 3b = 1

Add '5' to each side of the equation.
-5 + 5 + 3b = 1 + 5

Combine like terms: -5 + 5 = 0
0 + 3b = 1 + 5
3b = 1 + 5

Combine like terms: 1 + 5 = 6
3b = 6

Divide each side by '3'.
b = 2

Simplifying
b = 2

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