15b^2+6b-3=

Solution for 15b^2+6b-3= equation:

Simplifying
15b2 + 6b + -3 = 0

Reorder the terms:
-3 + 6b + 15b2 = 0

Solving
-3 + 6b + 15b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + 2b + 5b2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-1 + 2b + 5b2)' equal to zero and attempt to solve:

Simplifying
-1 + 2b + 5b2 = 0

Solving
-1 + 2b + 5b2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-0.2 + 0.4b + b2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.4b + 0.2 + b2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.4b + b2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.4b + b2 = 0 + 0.2
0.4b + b2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.4b + b2 = 0.2

The b term is 0.4b.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4b + 0.04 + b2 = 0.2 + 0.04

Reorder the terms:
0.04 + 0.4b + b2 = 0.2 + 0.04

Combine like terms: 0.2 + 0.04 = 0.24
0.04 + 0.4b + b2 = 0.24

Factor a perfect square on the left side:
(b + 0.2)(b + 0.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(b + 0.2) equal to 0.489897949 and -0.489897949.

Subproblem 1
b + 0.2 = 0.489897949

Simplifying
b + 0.2 = 0.489897949

Reorder the terms:
0.2 + b = 0.489897949

Solving
0.2 + b = 0.489897949

Solving for variable 'b'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + b = 0.489897949 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + b = 0.489897949 + -0.2
b = 0.489897949 + -0.2

Combine like terms: 0.489897949 + -0.2 = 0.289897949
b = 0.289897949

Simplifying
b = 0.289897949

Subproblem 2
b + 0.2 = -0.489897949

Simplifying
b + 0.2 = -0.489897949

Reorder the terms:
0.2 + b = -0.489897949

Solving
0.2 + b = -0.489897949

Solving for variable 'b'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + b = -0.489897949 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + b = -0.489897949 + -0.2
b = -0.489897949 + -0.2

Combine like terms: -0.489897949 + -0.2 = -0.689897949
b = -0.689897949

Simplifying
b = -0.689897949

Solution
The solution to the problem is based on the solutions
from the subproblems.
b = {0.289897949, -0.689897949}
Solution
b = {0.289897949, -0.689897949}