(b+2)(b-5)=18

Solution for (b+2)(b-5)=18 equation:

Simplifying
(b + 2)(b + -5) = 18

Reorder the terms:
(2 + b)(b + -5) = 18

Reorder the terms:
(2 + b)(-5 + b) = 18

Multiply (2 + b) * (-5 + b)
(2(-5 + b) + b(-5 + b)) = 18
((-5 * 2 + b * 2) + b(-5 + b)) = 18
((-10 + 2b) + b(-5 + b)) = 18
(-10 + 2b + (-5 * b + b * b)) = 18
(-10 + 2b + (-5b + b2)) = 18

Combine like terms: 2b + -5b = -3b
(-10 + -3b + b2) = 18

Solving
-10 + -3b + b2 = 18

Solving for variable 'b'.

Reorder the terms:
-10 + -18 + -3b + b2 = 18 + -18

Combine like terms: -10 + -18 = -28
-28 + -3b + b2 = 18 + -18

Combine like terms: 18 + -18 = 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}