28b^2=160b+48

Solution for 28b^2=160b+48 equation:

Simplifying
28b2 = 160b + 48

Reorder the terms:
28b2 = 48 + 160b

Solving
28b2 = 48 + 160b

Solving for variable 'b'.

Reorder the terms:
-48 + -160b + 28b2 = 48 + 160b + -48 + -160b

Reorder the terms:
-48 + -160b + 28b2 = 48 + -48 + 160b + -160b

Combine like terms: 48 + -48 = 0
-48 + -160b + 28b2 = 0 + 160b + -160b
-48 + -160b + 28b2 = 160b + -160b

Combine like terms: 160b + -160b = 0
-48 + -160b + 28b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + -40b + 7b2) = 0

Factor a trinomial.
4((-2 + -7b)(6 + -1b)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-2 + -7b)' equal to zero and attempt to solve:

Simplifying
-2 + -7b = 0

Solving
-2 + -7b = 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 + -7b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7b = 0 + 2
-7b = 0 + 2

Combine like terms: 0 + 2 = 2
-7b = 2

Divide each side by '-7'.
b = -0.2857142857

Simplifying
b = -0.2857142857
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {-0.2857142857, 6}