(b+7)+(3b-3)(b-6)=

Solution for (b+7)+(3b-3)(b-6)= equation:

Simplifying
(b + 7) + (3b + -3)(b + -6) = 0

Reorder the terms:
(7 + b) + (3b + -3)(b + -6) = 0

Remove parenthesis around (7 + b)
7 + b + (3b + -3)(b + -6) = 0

Reorder the terms:
7 + b + (-3 + 3b)(b + -6) = 0

Reorder the terms:
7 + b + (-3 + 3b)(-6 + b) = 0

Multiply (-3 + 3b) * (-6 + b)
7 + b + (-3(-6 + b) + 3b * (-6 + b)) = 0
7 + b + ((-6 * -3 + b * -3) + 3b * (-6 + b)) = 0
7 + b + ((18 + -3b) + 3b * (-6 + b)) = 0
7 + b + (18 + -3b + (-6 * 3b + b * 3b)) = 0
7 + b + (18 + -3b + (-18b + 3b2)) = 0

Combine like terms: -3b + -18b = -21b
7 + b + (18 + -21b + 3b2) = 0

Reorder the terms:
7 + 18 + b + -21b + 3b2 = 0

Combine like terms: 7 + 18 = 25
25 + b + -21b + 3b2 = 0

Combine like terms: b + -21b = -20b
25 + -20b + 3b2 = 0

Solving
25 + -20b + 3b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(5 + -3b)(5 + -1b) = 0

Subproblem 1
Set the factor '(5 + -3b)' equal to zero and attempt to solve:

Simplifying
5 + -3b = 0

Solving
5 + -3b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3b = 0 + -5

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

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

Divide each side by '-3'.
b = 1.666666667

Simplifying
b = 1.666666667
Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1b = 0 + -5

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

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

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {1.666666667, 5}