b^2+6b+9=-4b+48

Solution for b^2+6b+9=-4b+48 equation:

Simplifying
b2 + 6b + 9 = -4b + 48

Reorder the terms:
9 + 6b + b2 = -4b + 48

Reorder the terms:
9 + 6b + b2 = 48 + -4b

Solving
9 + 6b + b2 = 48 + -4b

Solving for variable 'b'.

Reorder the terms:
9 + -48 + 6b + 4b + b2 = 48 + -4b + -48 + 4b

Combine like terms: 9 + -48 = -39
-39 + 6b + 4b + b2 = 48 + -4b + -48 + 4b

Combine like terms: 6b + 4b = 10b
-39 + 10b + b2 = 48 + -4b + -48 + 4b

Reorder the terms:
-39 + 10b + b2 = 48 + -48 + -4b + 4b

Combine like terms: 48 + -48 = 0
-39 + 10b + b2 = 0 + -4b + 4b
-39 + 10b + b2 = -4b + 4b

Combine like terms: -4b + 4b = 0
-39 + 10b + b2 = 0

Factor a trinomial.
(-13 + -1b)(3 + -1b) = 0

Subproblem 1
Set the factor '(-13 + -1b)' equal to zero and attempt to solve:

Simplifying
-13 + -1b = 0

Solving
-13 + -1b = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1b = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1b = 0 + 13
-1b = 0 + 13

Combine like terms: 0 + 13 = 13
-1b = 13

Divide each side by '-1'.
b = -13

Simplifying
b = -13
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 = {-13, 3}