2b^2+24b+144=72

Solution for 2b^2+24b+144=72 equation:

Simplifying
2b2 + 24b + 144 = 72

Reorder the terms:
144 + 24b + 2b2 = 72

Solving
144 + 24b + 2b2 = 72

Solving for variable 'b'.

Reorder the terms:
144 + -72 + 24b + 2b2 = 72 + -72

Combine like terms: 144 + -72 = 72
72 + 24b + 2b2 = 72 + -72

Combine like terms: 72 + -72 = 0
72 + 24b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 12b + b2) = 0

Factor a trinomial.
2((6 + b)(6 + b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + b)' equal to zero and attempt to solve:

Simplifying
6 + b = 0

Solving
6 + b = 0

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

Add '-6' to each side of the equation.
6 + -6 + b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + b = 0 + -6
b = 0 + -6

Combine like terms: 0 + -6 = -6
b = -6

Simplifying
b = -6
Subproblem 2
Set the factor '(6 + b)' equal to zero and attempt to solve:

Simplifying
6 + b = 0

Solving
6 + b = 0

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

Add '-6' to each side of the equation.
6 + -6 + b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + b = 0 + -6
b = 0 + -6

Combine like terms: 0 + -6 = -6
b = -6

Simplifying
b = -6
Solution
b = {-6, -6}