3b^2=15b-12

Solution for 3b^2=15b-12 equation:

Simplifying
3b2 = 15b + -12

Reorder the terms:
3b2 = -12 + 15b

Solving
3b2 = -12 + 15b

Solving for variable 'b'.

Reorder the terms:
12 + -15b + 3b2 = -12 + 15b + 12 + -15b

Reorder the terms:
12 + -15b + 3b2 = -12 + 12 + 15b + -15b

Combine like terms: -12 + 12 = 0
12 + -15b + 3b2 = 0 + 15b + -15b
12 + -15b + 3b2 = 15b + -15b

Combine like terms: 15b + -15b = 0
12 + -15b + 3b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -5b + b2) = 0

Factor a trinomial.
3((1 + -1b)(4 + -1b)) = 0

Ignore the factor 3.
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 '(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 = {1, 4}