4b^2-7b-30=0

Solution for 4b^2-7b-30=0 equation:

Simplifying
4b2 + -7b + -30 = 0

Reorder the terms:
-30 + -7b + 4b2 = 0

Solving
-30 + -7b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-2 + -1b)(15 + -4b) = 0

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

Simplifying
-2 + -1b = 0

Solving
-2 + -1b = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1b = 0 + 2
-1b = 0 + 2

Combine like terms: 0 + 2 = 2
-1b = 2

Divide each side by '-1'.
b = -2

Simplifying
b = -2
Subproblem 2
Set the factor '(15 + -4b)' equal to zero and attempt to solve:

Simplifying
15 + -4b = 0

Solving
15 + -4b = 0

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

Add '-15' to each side of the equation.
15 + -15 + -4b = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -4b = 0 + -15
-4b = 0 + -15

Combine like terms: 0 + -15 = -15
-4b = -15

Divide each side by '-4'.
b = 3.75

Simplifying
b = 3.75
Solution
b = {-2, 3.75}