3b^2-7b=48

Solution for 3b^2-7b=48 equation:

Simplifying
3b2 + -7b = 48

Reorder the terms:
-7b + 3b2 = 48

Solving
-7b + 3b2 = 48

Solving for variable 'b'.

Reorder the terms:
-48 + -7b + 3b2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + -7b + 3b2 = 0

Factor a trinomial.
(-3 + -1b)(16 + -3b) = 0

Subproblem 1
Set the factor '(-3 + -1b)' equal to zero and attempt to solve:

Simplifying
-3 + -1b = 0

Solving
-3 + -1b = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1b = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1b = 0 + 3
-1b = 0 + 3

Combine like terms: 0 + 3 = 3
-1b = 3

Divide each side by '-1'.
b = -3

Simplifying
b = -3
Subproblem 2
Set the factor '(16 + -3b)' equal to zero and attempt to solve:

Simplifying
16 + -3b = 0

Solving
16 + -3b = 0

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

Add '-16' to each side of the equation.
16 + -16 + -3b = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -3b = 0 + -16
-3b = 0 + -16

Combine like terms: 0 + -16 = -16
-3b = -16

Divide each side by '-3'.
b = 5.333333333

Simplifying
b = 5.333333333
Solution
b = {-3, 5.333333333}