(b-7)(b+4)=0

Solution for (b-7)(b+4)=0 equation:

Simplifying
(b + -7)(b + 4) = 0

Reorder the terms:
(-7 + b)(b + 4) = 0

Reorder the terms:
(-7 + b)(4 + b) = 0

Multiply (-7 + b) * (4 + b)
(-7(4 + b) + b(4 + b)) = 0
((4 * -7 + b * -7) + b(4 + b)) = 0
((-28 + -7b) + b(4 + b)) = 0
(-28 + -7b + (4 * b + b * b)) = 0
(-28 + -7b + (4b + b2)) = 0

Combine like terms: -7b + 4b = -3b
(-28 + -3b + b2) = 0

Solving
-28 + -3b + b2 = 0

Solving for variable 'b'.

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}