.5(b)(2b+8)=21

Solution for .5(b)(2b+8)=21 equation:

Simplifying
0.5(b)(2b + 8) = 21

Reorder the terms:
0.5b(8 + 2b) = 21
(8 * 0.5b + 2b * 0.5b) = 21
(4b + 1b2) = 21

Solving
4b + 1b2 = 21

Solving for variable 'b'.

Reorder the terms:
-21 + 4b + 1b2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + 4b + 1b2 = 0

Factor a trinomial.
(-7 + -1b)(3 + -1b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-7, 3}