b^2+10b+31=7

Solution for b^2+10b+31=7 equation:

Simplifying
b2 + 10b + 31 = 7

Reorder the terms:
31 + 10b + b2 = 7

Solving
31 + 10b + b2 = 7

Solving for variable 'b'.

Reorder the terms:
31 + -7 + 10b + b2 = 7 + -7

Combine like terms: 31 + -7 = 24
24 + 10b + b2 = 7 + -7

Combine like terms: 7 + -7 = 0
24 + 10b + b2 = 0

Factor a trinomial.
(6 + b)(4 + b) = 0

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 '(4 + b)' equal to zero and attempt to solve:

Simplifying
4 + b = 0

Solving
4 + b = 0

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

Add '-4' to each side of the equation.
4 + -4 + b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + b = 0 + -4
b = 0 + -4

Combine like terms: 0 + -4 = -4
b = -4

Simplifying
b = -4
Solution
b = {-6, -4}