4b^2+7b-65=0

Solution for 4b^2+7b-65=0 equation:

Simplifying
4b2 + 7b + -65 = 0

Reorder the terms:
-65 + 7b + 4b2 = 0

Solving
-65 + 7b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-5 + -1b)(13 + -4b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(13 + -4b)' equal to zero and attempt to solve:

Simplifying
13 + -4b = 0

Solving
13 + -4b = 0

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

Add '-13' to each side of the equation.
13 + -13 + -4b = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -4b = 0 + -13
-4b = 0 + -13

Combine like terms: 0 + -13 = -13
-4b = -13

Divide each side by '-4'.
b = 3.25

Simplifying
b = 3.25
Solution
b = {-5, 3.25}