4b^2-48b-25=0

Solution for 4b^2-48b-25=0 equation:

Simplifying
4b2 + -48b + -25 = 0

Reorder the terms:
-25 + -48b + 4b2 = 0

Solving
-25 + -48b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-1 + -2b)(25 + -2b) = 0

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

Simplifying
-1 + -2b = 0

Solving
-1 + -2b = 0

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

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

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

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

Divide each side by '-2'.
b = -0.5

Simplifying
b = -0.5
Subproblem 2
Set the factor '(25 + -2b)' equal to zero and attempt to solve:

Simplifying
25 + -2b = 0

Solving
25 + -2b = 0

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

Add '-25' to each side of the equation.
25 + -25 + -2b = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -2b = 0 + -25
-2b = 0 + -25

Combine like terms: 0 + -25 = -25
-2b = -25

Divide each side by '-2'.
b = 12.5

Simplifying
b = 12.5
Solution
b = {-0.5, 12.5}