15b^2-12=-3b

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

Simplifying
15b2 + -12 = -3b

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

Solving
-12 + 15b2 = -3b

Solving for variable 'b'.

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

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

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

Factor a trinomial.
3((-1 + -1b)(4 + -5b)) = 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 + -5b)' equal to zero and attempt to solve:

Simplifying
4 + -5b = 0

Solving
4 + -5b = 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 + -5b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5b = 0 + -4
-5b = 0 + -4

Combine like terms: 0 + -4 = -4
-5b = -4

Divide each side by '-5'.
b = 0.8

Simplifying
b = 0.8
Solution
b = {-1, 0.8}