7b^2-27b-40=0

Solution for 7b^2-27b-40=0 equation:

Simplifying
7b2 + -27b + -40 = 0

Reorder the terms:
-40 + -27b + 7b2 = 0

Solving
-40 + -27b + 7b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-8 + -7b)(5 + -1b) = 0

Subproblem 1
Set the factor '(-8 + -7b)' equal to zero and attempt to solve:

Simplifying
-8 + -7b = 0

Solving
-8 + -7b = 0

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

Add '8' to each side of the equation.
-8 + 8 + -7b = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7b = 0 + 8
-7b = 0 + 8

Combine like terms: 0 + 8 = 8
-7b = 8

Divide each side by '-7'.
b = -1.142857143

Simplifying
b = -1.142857143
Subproblem 2
Set the factor '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

Simplifying
b = 5
Solution
b = {-1.142857143, 5}