2b^2+9b+16=7

Solution for 2b^2+9b+16=7 equation:

Simplifying
2b2 + 9b + 16 = 7

Reorder the terms:
16 + 9b + 2b2 = 7

Solving
16 + 9b + 2b2 = 7

Solving for variable 'b'.

Reorder the terms:
16 + -7 + 9b + 2b2 = 7 + -7

Combine like terms: 16 + -7 = 9
9 + 9b + 2b2 = 7 + -7

Combine like terms: 7 + -7 = 0
9 + 9b + 2b2 = 0

Factor a trinomial.
(3 + b)(3 + 2b) = 0

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

Simplifying
3 + b = 0

Solving
3 + b = 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 + b = 0 + -3

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

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

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

Simplifying
3 + 2b = 0

Solving
3 + 2b = 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 + 2b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2b = 0 + -3
2b = 0 + -3

Combine like terms: 0 + -3 = -3
2b = -3

Divide each side by '2'.
b = -1.5

Simplifying
b = -1.5
Solution
b = {-3, -1.5}