(b+2)(b-2)=(b+8)(6-3)

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Solution for (b+2)(b-2)=(b+8)(6-3) equation: 


Simplifying
(b + 2)(b + -2) = (b + 8)(6 + -3)

Reorder the terms:
(2 + b)(b + -2) = (b + 8)(6 + -3)

Reorder the terms:
(2 + b)(-2 + b) = (b + 8)(6 + -3)

Multiply (2 + b) * (-2 + b)
(2(-2 + b) + b(-2 + b)) = (b + 8)(6 + -3)
((-2 * 2 + b * 2) + b(-2 + b)) = (b + 8)(6 + -3)
((-4 + 2b) + b(-2 + b)) = (b + 8)(6 + -3)
(-4 + 2b + (-2 * b + b * b)) = (b + 8)(6 + -3)
(-4 + 2b + (-2b + b2)) = (b + 8)(6 + -3)

Combine like terms: 2b + -2b = 0
(-4 + 0 + b2) = (b + 8)(6 + -3)
(-4 + b2) = (b + 8)(6 + -3)

Reorder the terms:
-4 + b2 = (8 + b)(6 + -3)

Combine like terms: 6 + -3 = 3
-4 + b2 = (8 + b)(3)

Reorder the terms for easier multiplication:
-4 + b2 = 3(8 + b)
-4 + b2 = (8 * 3 + b * 3)
-4 + b2 = (24 + 3b)

Solving
-4 + b2 = 24 + 3b

Solving for variable 'b'.

Reorder the terms:
-4 + -24 + -3b + b2 = 24 + 3b + -24 + -3b

Combine like terms: -4 + -24 = -28
-28 + -3b + b2 = 24 + 3b + -24 + -3b

Reorder the terms:
-28 + -3b + b2 = 24 + -24 + 3b + -3b

Combine like terms: 24 + -24 = 0
-28 + -3b + b2 = 0 + 3b + -3b
-28 + -3b + b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
-28 + -3b + b2 = 0

Factor a trinomial.
(-4 + -1b)(7 + -1b) = 0


Subproblem 1
Set the factor '(-4 + -1b)' equal to zero and attempt to solve:

Simplifying
-4 + -1b = 0

Solving
-4 + -1b = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1b = 0 + 4
-1b = 0 + 4

Combine like terms: 0 + 4 = 4
-1b = 4

Divide each side by '-1'.
b = -4

Simplifying
b = -4

Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {-4, 7}

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