30b^2=78b-48

Solution for 30b^2=78b-48 equation:

Simplifying
30b2 = 78b + -48

Reorder the terms:
30b2 = -48 + 78b

Solving
30b2 = -48 + 78b

Solving for variable 'b'.

Reorder the terms:
48 + -78b + 30b2 = -48 + 78b + 48 + -78b

Reorder the terms:
48 + -78b + 30b2 = -48 + 48 + 78b + -78b

Combine like terms: -48 + 48 = 0
48 + -78b + 30b2 = 0 + 78b + -78b
48 + -78b + 30b2 = 78b + -78b

Combine like terms: 78b + -78b = 0
48 + -78b + 30b2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + -13b + 5b2) = 0

Factor a trinomial.
6((1 + -1b)(8 + -5b)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -1b)' equal to zero and attempt to solve:

Simplifying
1 + -1b = 0

Solving
1 + -1b = 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 + -1b = 0 + -1

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

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

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

Simplifying
b = 1
Subproblem 2
Set the factor '(8 + -5b)' equal to zero and attempt to solve:

Simplifying
8 + -5b = 0

Solving
8 + -5b = 0

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

Add '-8' to each side of the equation.
8 + -8 + -5b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5b = 0 + -8
-5b = 0 + -8

Combine like terms: 0 + -8 = -8
-5b = -8

Divide each side by '-5'.
b = 1.6

Simplifying
b = 1.6
Solution
b = {1, 1.6}