(B-1)(8B+31)=5

Solution for (B-1)(8B+31)=5 equation:

Simplifying
(B + -1)(8B + 31) = 5

Reorder the terms:
(-1 + B)(8B + 31) = 5

Reorder the terms:
(-1 + B)(31 + 8B) = 5

Multiply (-1 + B) * (31 + 8B)
(-1(31 + 8B) + B(31 + 8B)) = 5
((31 * -1 + 8B * -1) + B(31 + 8B)) = 5
((-31 + -8B) + B(31 + 8B)) = 5
(-31 + -8B + (31 * B + 8B * B)) = 5
(-31 + -8B + (31B + 8B2)) = 5

Combine like terms: -8B + 31B = 23B
(-31 + 23B + 8B2) = 5

Solving
-31 + 23B + 8B2 = 5

Solving for variable 'B'.

Reorder the terms:
-31 + -5 + 23B + 8B2 = 5 + -5

Combine like terms: -31 + -5 = -36
-36 + 23B + 8B2 = 5 + -5

Combine like terms: 5 + -5 = 0
-36 + 23B + 8B2 = 0

Factor a trinomial.
(-4 + -1B)(9 + -8B) = 0

Subproblem 1
Set the factor '(-4 + -1B)' equal to zero and attempt to solve:

Simplifying
-4 + -1B = 0

Solving
-4 + -1B = 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 + -1B = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1B = 0 + 4
-1B = 0 + 4

Combine like terms: 0 + 4 = 4
-1B = 4

Divide each side by '-1'.
B = -4

Simplifying
B = -4
Subproblem 2
Set the factor '(9 + -8B)' equal to zero and attempt to solve:

Simplifying
9 + -8B = 0

Solving
9 + -8B = 0

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

Add '-9' to each side of the equation.
9 + -9 + -8B = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8B = 0 + -9
-8B = 0 + -9

Combine like terms: 0 + -9 = -9
-8B = -9

Divide each side by '-8'.
B = 1.125

Simplifying
B = 1.125
Solution
B = {-4, 1.125}