(b-5)(b+2)=-12

Solution for (b-5)(b+2)=-12 equation:

Simplifying
(b + -5)(b + 2) = -12

Reorder the terms:
(-5 + b)(b + 2) = -12

Reorder the terms:
(-5 + b)(2 + b) = -12

Multiply (-5 + b) * (2 + b)
(-5(2 + b) + b(2 + b)) = -12
((2 * -5 + b * -5) + b(2 + b)) = -12
((-10 + -5b) + b(2 + b)) = -12
(-10 + -5b + (2 * b + b * b)) = -12
(-10 + -5b + (2b + b2)) = -12

Combine like terms: -5b + 2b = -3b
(-10 + -3b + b2) = -12

Solving
-10 + -3b + b2 = -12

Solving for variable 'b'.

Reorder the terms:
-10 + 12 + -3b + b2 = -12 + 12

Combine like terms: -10 + 12 = 2
2 + -3b + b2 = -12 + 12

Combine like terms: -12 + 12 = 0
2 + -3b + b2 = 0

Factor a trinomial.
(1 + -1b)(2 + -1b) = 0

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

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

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

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

Simplifying
2 + -1b = 0

Solving
2 + -1b = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1b = 0 + -2
-1b = 0 + -2

Combine like terms: 0 + -2 = -2
-1b = -2

Divide each side by '-1'.
b = 2

Simplifying
b = 2
Solution
b = {1, 2}