3b^2=4b+15

Solution for 3b^2=4b+15 equation:

Simplifying
3b2 = 4b + 15

Reorder the terms:
3b2 = 15 + 4b

Solving
3b2 = 15 + 4b

Solving for variable 'b'.

Reorder the terms:
-15 + -4b + 3b2 = 15 + 4b + -15 + -4b

Reorder the terms:
-15 + -4b + 3b2 = 15 + -15 + 4b + -4b

Combine like terms: 15 + -15 = 0
-15 + -4b + 3b2 = 0 + 4b + -4b
-15 + -4b + 3b2 = 4b + -4b

Combine like terms: 4b + -4b = 0
-15 + -4b + 3b2 = 0

Factor a trinomial.
(-5 + -3b)(3 + -1b) = 0

Subproblem 1
Set the factor '(-5 + -3b)' equal to zero and attempt to solve:

Simplifying
-5 + -3b = 0

Solving
-5 + -3b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3b = 0 + 5
-3b = 0 + 5

Combine like terms: 0 + 5 = 5
-3b = 5

Divide each side by '-3'.
b = -1.666666667

Simplifying
b = -1.666666667
Subproblem 2
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
Solution
b = {-1.666666667, 3}