2b^2+10b+15=3

Solution for 2b^2+10b+15=3 equation:

Simplifying
2b2 + 10b + 15 = 3

Reorder the terms:
15 + 10b + 2b2 = 3

Solving
15 + 10b + 2b2 = 3

Solving for variable 'b'.

Reorder the terms:
15 + -3 + 10b + 2b2 = 3 + -3

Combine like terms: 15 + -3 = 12
12 + 10b + 2b2 = 3 + -3

Combine like terms: 3 + -3 = 0
12 + 10b + 2b2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + 5b + b2) = 0

Factor a trinomial.
2((3 + b)(2 + b)) = 0

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

Simplifying
3 + b = 0

Solving
3 + b = 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 + b = 0 + -3

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

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

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

Simplifying
2 + b = 0

Solving
2 + b = 0

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

Add '-2' to each side of the equation.
2 + -2 + b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + b = 0 + -2
b = 0 + -2

Combine like terms: 0 + -2 = -2
b = -2

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