b^2+24b+144=729

Solution for b^2+24b+144=729 equation:

Simplifying
b2 + 24b + 144 = 729

Reorder the terms:
144 + 24b + b2 = 729

Solving
144 + 24b + b2 = 729

Solving for variable 'b'.

Reorder the terms:
144 + -729 + 24b + b2 = 729 + -729

Combine like terms: 144 + -729 = -585
-585 + 24b + b2 = 729 + -729

Combine like terms: 729 + -729 = 0
-585 + 24b + b2 = 0

Factor a trinomial.
(-39 + -1b)(15 + -1b) = 0

Subproblem 1
Set the factor '(-39 + -1b)' equal to zero and attempt to solve:

Simplifying
-39 + -1b = 0

Solving
-39 + -1b = 0

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

Add '39' to each side of the equation.
-39 + 39 + -1b = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -1b = 0 + 39
-1b = 0 + 39

Combine like terms: 0 + 39 = 39
-1b = 39

Divide each side by '-1'.
b = -39

Simplifying
b = -39
Subproblem 2
Set the factor '(15 + -1b)' equal to zero and attempt to solve:

Simplifying
15 + -1b = 0

Solving
15 + -1b = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1b = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1b = 0 + -15
-1b = 0 + -15

Combine like terms: 0 + -15 = -15
-1b = -15

Divide each side by '-1'.
b = 15

Simplifying
b = 15
Solution
b = {-39, 15}