5b+15=2b(b+3)

Solution for 5b+15=2b(b+3) equation:

Simplifying
5b + 15 = 2b(b + 3)

Reorder the terms:
15 + 5b = 2b(b + 3)

Reorder the terms:
15 + 5b = 2b(3 + b)
15 + 5b = (3 * 2b + b * 2b)
15 + 5b = (6b + 2b2)

Solving
15 + 5b = 6b + 2b2

Solving for variable 'b'.

Combine like terms: 5b + -6b = -1b
15 + -1b + -2b2 = 6b + 2b2 + -6b + -2b2

Reorder the terms:
15 + -1b + -2b2 = 6b + -6b + 2b2 + -2b2

Combine like terms: 6b + -6b = 0
15 + -1b + -2b2 = 0 + 2b2 + -2b2
15 + -1b + -2b2 = 2b2 + -2b2

Combine like terms: 2b2 + -2b2 = 0
15 + -1b + -2b2 = 0

Factor a trinomial.
(5 + -2b)(3 + b) = 0

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

Simplifying
5 + -2b = 0

Solving
5 + -2b = 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 + -2b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2b = 0 + -5
-2b = 0 + -5

Combine like terms: 0 + -5 = -5
-2b = -5

Divide each side by '-2'.
b = 2.5

Simplifying
b = 2.5
Subproblem 2
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
Solution
b = {2.5, -3}