(b+7)*(b-6)=(b+2)*(b-9)

Solution for (b+7)*(b-6)=(b+2)*(b-9) equation:

Simplifying
(b + 7)(b + -6) = (b + 2)(b + -9)

Reorder the terms:
(7 + b)(b + -6) = (b + 2)(b + -9)

Reorder the terms:
(7 + b)(-6 + b) = (b + 2)(b + -9)

Multiply (7 + b) * (-6 + b)
(7(-6 + b) + b(-6 + b)) = (b + 2)(b + -9)
((-6 * 7 + b * 7) + b(-6 + b)) = (b + 2)(b + -9)
((-42 + 7b) + b(-6 + b)) = (b + 2)(b + -9)
(-42 + 7b + (-6 * b + b * b)) = (b + 2)(b + -9)
(-42 + 7b + (-6b + b2)) = (b + 2)(b + -9)

Combine like terms: 7b + -6b = 1b
(-42 + 1b + b2) = (b + 2)(b + -9)

Reorder the terms:
-42 + 1b + b2 = (2 + b)(b + -9)

Reorder the terms:
-42 + 1b + b2 = (2 + b)(-9 + b)

Multiply (2 + b) * (-9 + b)
-42 + 1b + b2 = (2(-9 + b) + b(-9 + b))
-42 + 1b + b2 = ((-9 * 2 + b * 2) + b(-9 + b))
-42 + 1b + b2 = ((-18 + 2b) + b(-9 + b))
-42 + 1b + b2 = (-18 + 2b + (-9 * b + b * b))
-42 + 1b + b2 = (-18 + 2b + (-9b + b2))

Combine like terms: 2b + -9b = -7b
-42 + 1b + b2 = (-18 + -7b + b2)

Add '-1b2' to each side of the equation.
-42 + 1b + b2 + -1b2 = -18 + -7b + b2 + -1b2

Combine like terms: b2 + -1b2 = 0
-42 + 1b + 0 = -18 + -7b + b2 + -1b2
-42 + 1b = -18 + -7b + b2 + -1b2

Combine like terms: b2 + -1b2 = 0
-42 + 1b = -18 + -7b + 0
-42 + 1b = -18 + -7b

Solving
-42 + 1b = -18 + -7b

Solving for variable 'b'.

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

Add '7b' to each side of the equation.
-42 + 1b + 7b = -18 + -7b + 7b

Combine like terms: 1b + 7b = 8b
-42 + 8b = -18 + -7b + 7b

Combine like terms: -7b + 7b = 0
-42 + 8b = -18 + 0
-42 + 8b = -18

Add '42' to each side of the equation.
-42 + 42 + 8b = -18 + 42

Combine like terms: -42 + 42 = 0
0 + 8b = -18 + 42
8b = -18 + 42

Combine like terms: -18 + 42 = 24
8b = 24

Divide each side by '8'.
b = 3

Simplifying
b = 3