28b^2+32=120b

Solution for 28b^2+32=120b equation:

Simplifying
28b2 + 32 = 120b

Reorder the terms:
32 + 28b2 = 120b

Solving
32 + 28b2 = 120b

Solving for variable 'b'.

Reorder the terms:
32 + -120b + 28b2 = 120b + -120b

Combine like terms: 120b + -120b = 0
32 + -120b + 28b2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(8 + -30b + 7b2) = 0

Factor a trinomial.
4((2 + -7b)(4 + -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 '(4 + -1b)' equal to zero and attempt to solve:

Simplifying
4 + -1b = 0

Solving
4 + -1b = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1b = 0 + -4
-1b = 0 + -4

Combine like terms: 0 + -4 = -4
-1b = -4

Divide each side by '-1'.
b = 4

Simplifying
b = 4
Solution
b = {0.2857142857, 4}